. . "1117659210"^^ . . "In matematica, un problema di Dirichlet richiede di trovare una funzione che soddisfa una determinata equazione differenziale alle derivate parziali (PDE) all'interno di una regione sulla cui frontiera la funzione assume determinati valori al contorno. In origine il problema fu introdotto specificatamente per l'equazione di Laplace, ma pu\u00F2 essere posto per molte PDE. Relativamente all'equazione di Laplace, data una funzione che assume valori ovunque sul bordo di una regione in , il problema riguarda l'esistenza di un'unica funzione continua differenziabile due volte con continuit\u00E0 all'interno della regione, e continua sul bordo, tale che sia una funzione armonica all'interno e coincida con sul bordo. Tale richiesta \u00E8 detta condizione al contorno di Dirichlet."@it . . "In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally it was posed for Laplace's equation. In that case the problem can be stated as follows: This requirement is called the Dirichlet boundary condition. The main issue is to prove the existence of a solution; uniqueness can be proved using the maximum principle."@en . "Dirichlet Problem"@en . "\u5728\u6570\u5B66\u4E2D\uFF0C\u72C4\u5229\u514B\u96F7\u8FB9\u754C\u6761\u4EF6\uFF08Dirichlet boundary condition\uFF09\u4E5F\u88AB\u79F0\u4E3A\u5E38\u5FAE\u5206\u65B9\u7A0B\u6216\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u201C\u7B2C\u4E00\u7C7B\u8FB9\u754C\u6761\u4EF6\u201D\uFF0C\u6307\u5B9A\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u5728\u8FB9\u754C\u5904\u7684\u503C\u3002\u6C42\u51FA\u8FD9\u6837\u7684\u65B9\u7A0B\u7684\u89E3\u7684\u95EE\u9898\u88AB\u79F0\u4E3A\u72C4\u5229\u514B\u96F7\u95EE\u9898\u3002"@zh . . "\u6570\u5B66\u4E2D\uFF0C\u72C4\u5229\u514B\u96F7\u95EE\u9898\uFF08Dirichlet problem\uFF09\u662F\u5BFB\u627E\u4E00\u4E2A\u51FD\u6570\uFF0C\u4F7F\u5176\u4E3A\u7ED9\u5B9A\u533A\u57DF\u5185\u4E00\u4E2A\u6307\u5B9A\u7684\u504F\u5FAE\u5206\u65B9\u7A0B\uFF08PDE\uFF09\u7684\u89E3\uFF0C\u4E14\u5728\u8FB9\u754C\u4E0A\u53D6\u9884\u5B9A\u503C\u3002 \u5BF9\u8BB8\u591A\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u72C4\u5229\u514B\u96F7\u95EE\u9898\u90FD\u53EF\u89E3\uFF0C\u4F46\u6700\u521D\u662F\u5BF9\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u63D0\u51FA\u6765\u7684\u3002\u5728\u8FD9\u79CD\u60C5\u5F62\u4E0B\u95EE\u9898\u53EF\u5982\u4E0B\u8868\u8FF0\uFF1A \u7ED9\u5B9A\u5B9A\u4E49\u5728Rn\u4E2D\u4E00\u4E2A\u533A\u57DF\u7684\u8FB9\u754C\u4E0A\u4E00\u4E2A\u51FD\u6570f\uFF0C\u662F\u5426\u5B58\u5728\u60DF\u4E00\u8FDE\u7EED\u51FD\u6570u\u5728\u5185\u90E8\u4E24\u6B21\u8FDE\u7EED\u53EF\u5FAE\uFF0C\u5728\u8FB9\u754C\u4E0A\u8FDE\u7EED\uFF0C\u4F7F\u5F97u\u5728\u5185\u90E8\u8C03\u548C\u5E76\u5728\u8FB9\u754C\u4E0Au = f\uFF1F \u8FD9\u4E2A\u6761\u4EF6\u79F0\u4E3A\u72C4\u5229\u514B\u96F7\u8FB9\u754C\u6761\u4EF6\u3002\u6700\u4E3B\u8981\u7684\u95EE\u9898\u662F\u8BC1\u660E\u89E3\u7684\u5B58\u5728\u6027\uFF0C\u56E0\u552F\u4E00\u6027\u53EF\u5229\u7528\u8BC1\u660E\u3002"@zh . . . . "Problema de Dirichlet"@pt . . "Condizioni al contorno di Dirichlet"@it . "Problem Dirichleta polega na znalezieniu funkcji harmonicznej dla danego obszaru z danymi warto\u015Bciami na brzegu. Problem ten zosta\u0142 po raz pierwszy postawiony przez Lejeune\u2019a Dirichleta dla r\u00F3wnania Laplace\u2019a."@pl . . "Warunek brzegowy Dirichleta \u2013 typ warunku brzegowego, znany tak\u017Ce jako warunek pierwszego rodzaju, u\u017Cywanym w teorii r\u00F3wna\u0144 r\u00F3\u017Cniczkowych zwyczajnych lub cz\u0105stkowych. Polega on na za\u0142o\u017Ceniu, \u017Ce funkcja b\u0119d\u0105ca rozwi\u0105zaniem danego problemu musi przyjmowa\u0107 okre\u015Blone, z g\u00F3ry zadane warto\u015Bci na brzegu dziedziny. Nazwa pochodzi od matematyka P. Dirichleta (1805\u20131859). Je\u017Celi dla r\u00F3wnania r\u00F3\u017Cniczkowego (zwyczajnego lub cz\u0105stkowego) stawiamy warunek brzegowy Dirichleta (na ca\u0142ym brzegu), to m\u00F3wimy o zagadnieniu (problemie) Dirichleta."@pl . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0456\u0440\u0456\u0445\u043B\u0435 \u2014 \u0432\u0438\u0434 \u0437\u0430\u0434\u0430\u0447, \u0449\u043E \u0437'\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0438 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u0456 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0437 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u043C\u0438 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u043C\u0438 \u0434\u0440\u0443\u0433\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0419\u043E\u0433\u0430\u043D\u043D\u0430 \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . . "\u30C7\u30A3\u30EA\u30AF\u30EC\u5883\u754C\u6761\u4EF6\uFF08\u30C7\u30A3\u30EA\u30AF\u30EC\u304D\u3087\u3046\u304B\u3044\u3058\u3087\u3046\u3051\u3093\uFF09\u3042\u308B\u3044\u306F\u7B2C1\u7A2E\u5883\u754C\u6761\u4EF6\u306F\u3001\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u304A\u3051\u308B\u5883\u754C\u6761\u4EF6\u306E\u4E00\u3064\u306E\u5F62\u72B6\u3067\u3042\u308A\u3001\u5883\u754C\u6761\u4EF6\u4E0A\u306E\u70B9\u306E\u5024\u3092\u76F4\u306B\u4E0E\u3048\u308B\u3082\u306E\u3067\u3042\u308B\u3002 \u3088\u308A\u53B3\u5BC6\u306B\u8A00\u3046\u3068\u3001y \u306B\u95A2\u3059\u308B\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3067\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u5883\u754C\u4E0A\u306E\u70B9\u306E\u96C6\u5408\u3092 \u03A9 \u3068\u3057\u305F\u3068\u304D\u306B\u3001\u03A9 \u306B\u542B\u307E\u308C\u308B\u70B9 x \u304C\u3042\u308C\u3070 \u3068\u3044\u3046\u5F62\u3067\u8868\u73FE\u3067\u304D\u308B\u3088\u3046\u306A\u5883\u754C\u6761\u4EF6\u3067\u3042\u308B\u3002 \u4F8B\u3048\u3070\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F \u306B\u304A\u3044\u3066\u3001\u4E00\u822C\u89E3\u306F \u3068\u306A\u308B\u304C\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3068\u3057\u3066 y(0) = 1 \u3068\u3059\u308B\u3068\u3001 \u3068\u3044\u3046\u89E3\u304C\u5F97\u3089\u308C\u308B\u3002 \u306A\u304A\u3001\u4E00\u3064\u306E\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u304A\u3044\u3066\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u4EE5\u5916\u306E\u5883\u754C\u6761\u4EF6\u3068\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3092\u4F75\u7528\u3057\u3066\u8A2D\u5B9A\u3059\u308B\u3053\u3068\u3082\u73CD\u3057\u304F\u306A\u3044\u3002\u305F\u3060\u3057\u3001\u5C11\u306A\u304F\u3068\u3082\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3068\u540C\u7B49\u3068\u306A\u308B\u70B9\u304C1\u3064\u4EE5\u4E0A\u5B58\u5728\u3057\u306A\u3044\u5834\u5408\u306F\u3001\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u89E3\u304C\u6C7A\u5B9A\u3055\u308C\u306A\u3044\u3002"@ja . "Warunek brzegowy Dirichleta"@pl . . . . "En matem\u00E0tiques, el problema de Dirichlet consisteix a trobar una funci\u00F3 que resolgui una equaci\u00F3 diferencial parcial a l'interior d'una donada que t\u00E9 valors predeterminats al contorn de la regi\u00F3. Les condicions de frontera d'aquest problema s'anomenen Condicions de frontera de Dirichlet. El problema de Dirichlet es pot resoldre per moltes equacions diferencials parcials, tot i que en un primer moment va ser pensat per a l'equaci\u00F3 de Laplace. En aquest cas el problema es pot formular de la manera seg\u00FCent: Donada una funci\u00F3 f que pot ser avaluada en tots els contorns d'una regi\u00F3 Rn, nom\u00E9s hi ha una \u00FAnica funci\u00F3 cont\u00EDnua u derivable dues vegades en l'interior i cont\u00EDnua al contorn, tals que u \u00E9s una funci\u00F3 harm\u00F2nica a l'interior i u = f al contorn. Aquest requeriment s'anomena la condici\u00F3 de contorn de Dirichlet."@ca . . . . . . . "\u6570\u5B66\u4E2D\uFF0C\u72C4\u5229\u514B\u96F7\u95EE\u9898\uFF08Dirichlet problem\uFF09\u662F\u5BFB\u627E\u4E00\u4E2A\u51FD\u6570\uFF0C\u4F7F\u5176\u4E3A\u7ED9\u5B9A\u533A\u57DF\u5185\u4E00\u4E2A\u6307\u5B9A\u7684\u504F\u5FAE\u5206\u65B9\u7A0B\uFF08PDE\uFF09\u7684\u89E3\uFF0C\u4E14\u5728\u8FB9\u754C\u4E0A\u53D6\u9884\u5B9A\u503C\u3002 \u5BF9\u8BB8\u591A\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u72C4\u5229\u514B\u96F7\u95EE\u9898\u90FD\u53EF\u89E3\uFF0C\u4F46\u6700\u521D\u662F\u5BF9\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u63D0\u51FA\u6765\u7684\u3002\u5728\u8FD9\u79CD\u60C5\u5F62\u4E0B\u95EE\u9898\u53EF\u5982\u4E0B\u8868\u8FF0\uFF1A \u7ED9\u5B9A\u5B9A\u4E49\u5728Rn\u4E2D\u4E00\u4E2A\u533A\u57DF\u7684\u8FB9\u754C\u4E0A\u4E00\u4E2A\u51FD\u6570f\uFF0C\u662F\u5426\u5B58\u5728\u60DF\u4E00\u8FDE\u7EED\u51FD\u6570u\u5728\u5185\u90E8\u4E24\u6B21\u8FDE\u7EED\u53EF\u5FAE\uFF0C\u5728\u8FB9\u754C\u4E0A\u8FDE\u7EED\uFF0C\u4F7F\u5F97u\u5728\u5185\u90E8\u8C03\u548C\u5E76\u5728\u8FB9\u754C\u4E0Au = f\uFF1F \u8FD9\u4E2A\u6761\u4EF6\u79F0\u4E3A\u72C4\u5229\u514B\u96F7\u8FB9\u754C\u6761\u4EF6\u3002\u6700\u4E3B\u8981\u7684\u95EE\u9898\u662F\u8BC1\u660E\u89E3\u7684\u5B58\u5728\u6027\uFF0C\u56E0\u552F\u4E00\u6027\u53EF\u5229\u7528\u8BC1\u660E\u3002"@zh . "\u30C7\u30A3\u30EA\u30AF\u30EC\u5883\u754C\u6761\u4EF6"@ja . . . . . . . . . . . "En matem\u00E1ticas, el problema de Dirichlet es un problema que consiste en hallar una funci\u00F3n que es la soluci\u00F3n de una ecuaci\u00F3n en derivadas parciales (EDP) en el interior de un dominio de (o m\u00E1s generalmente una variedad diferenciable) que tome valores prescritos sobre el contorno de dicho dominio. El problema de Dirichlet puede resolverse para muchas EDPs, aunque originalmente fue planteada para la ecuaci\u00F3n de Laplace. En este caso el problema puede enunciarse como sigue: Este requisito se denomina condici\u00F3n de contorno de Dirichlet. En este problema es fundamental probar la existencia de la soluci\u00F3n; la unicidad viene dada utilizando el ."@es . . . . "Condici\u00F3n de frontera de Dirichlet"@es . . . "Probl\u00E8me de Dirichlet"@fr . "Als Dirichlet-Randbedingung (nach Peter Gustav Lejeune Dirichlet) bezeichnet man im Zusammenhang mit Differentialgleichungen (genauer: Randwertproblemen) Werte, die auf dem jeweiligen Rand des Definitionsbereichs von der Funktion angenommen werden sollen. Weitere Randbedingungen sind beispielsweise Neumann-Randbedingungen oder schiefe Randbedingungen."@de . . "\u0413\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0414\u0438\u0440\u0438\u0445\u043B\u0435"@ru . . . . . . . . . . "\uC218\uD559\uC5D0\uC11C \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74(Dirichlet boundary condition)\uC740 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uC758 \uC911\uC758 \uD558\uB098\uC774\uBA70, \uACBD\uACC4\uC5D0\uC11C \uC810\uC758 \uAC12\uC744 \uC9C1\uC811 \uC8FC\uB294 \uAC83\uC774\uB2E4. \uC218\uD559\uC790 \uD398\uD130 \uAD6C\uC2A4\uD0C0\uD504 \uB974\uC8C8 \uB514\uB9AC\uD074\uB808\uC758 \uC774\uB984\uC744 \uB530\uACE0 \uC788\uB2E4."@ko . "\uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74"@ko . . "\u30C7\u30A3\u30EA\u30AF\u30EC\u554F\u984C\uFF08\u82F1\u8A9E: Dirichlet problem\uFF09\u3068\u306F\u3001\u30E9\u30D7\u30E9\u30B9\u65B9\u7A0B\u5F0F\u3092\u3042\u308B\u9818\u57DF \u03A9 \u3067\u3001\u5883\u754C\u4E0A\u3067 \u03C6=G \u3068\u3044\u3046\u6761\u4EF6\u3067\u89E3\u3068\u306A\u308B\u8ABF\u548C\u95A2\u6570 \u03C6 = \u03C6(x1, x2, ..., xn) \u3092\u6C42\u3081\u308B\u554F\u984C\u3067\u3042\u308B\u3002\u7B2C\u4E00\u5883\u754C\u5024\u554F\u984C\u3068\u3082\u547C\u3070\u308C\u308B\u3002\u89E3\u6CD5\u306B\u306F\u3001\u30B0\u30EA\u30FC\u30F3\u95A2\u6570\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u306E\u539F\u7406\u3001\u4EA4\u4EE3\u6CD5\u3001\u30DD\u30A2\u30F3\u30AB\u30EC\u306E\u6383\u6563\u6CD5\u3001\u30DA\u30ED\u30F3\u6CD5\u306A\u3069\u304C\u3042\u308B\u3002"@ja . . "Dirichlet-Randbedingung"@de . . "\uC218\uD559\uC5D0\uC11C \uB514\uB9AC\uD074\uB808 \uBB38\uC81C(Dirichlet problem)\uB780 \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74\uC744 \uAC00\uC9C4 \uACBD\uACC4\uAC12 \uBB38\uC81C\uB2E4. \uC989, \uC8FC\uC5B4\uC9C4 \uC601\uC5ED\uC758 \uACBD\uACC4\uC5D0\uC11C\uC758 \uAC12\uC774 \uC870\uAC74\uC73C\uB85C \uC8FC\uC5B4\uC9C0\uB294 \uD2B9\uC815\uD55C \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC5D0 \uB300\uD558\uC5EC \uADF8 \uC601\uC5ED\uC758 \uB0B4\uBD80\uC5D0\uC11C\uC758 \uD574\uAC00 \uB420 \uC218 \uC788\uB294 \uD568\uC218\uB97C \uCC3E\uB294 \uBB38\uC81C\uC774\uB2E4. \uB514\uB9AC\uD074\uB808 \uBB38\uC81C\uB294 \uB9CE\uC740 \uC885\uB958\uC758 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uD480 \uC218 \uC788\uAC8C \uD558\uB294\uB370, \uC5ED\uC0AC\uC801\uC73C\uB85C \uB77C\uD50C\uB77C\uC2A4 \uBC29\uC815\uC2DD\uC744 \uD480\uC774\uD558\uAE30 \uC704\uD55C \uBC29\uBC95\uB860\uC73C\uB85C \uBC1C\uC804\uB418\uC5C8\uB2E4.\uC774\uB54C\uC758 \uC694\uAD6C\uB418\uB294 \uC870\uAC74\uC774 \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74\uC774\uB2E4. \uC8FC\uB85C \uD574\uC758 \uC874\uC7AC\uC131\uACFC \uC720\uC77C\uC131\uC774 \uC8FC\uC694\uD55C \uB17C\uC810\uC774 \uB418\uB294\uB370, \uC774\uAC83\uC740 \uCD5C\uB300 \uC6D0\uB9AC\uC5D0 \uC758\uD574 \uC99D\uBA85\uD560 \uC218 \uC788\uB2E4."@ko . . "A. Yanushauskas"@en . "En matem\u00E1ticas, el problema de Dirichlet es un problema que consiste en hallar una funci\u00F3n que es la soluci\u00F3n de una ecuaci\u00F3n en derivadas parciales (EDP) en el interior de un dominio de (o m\u00E1s generalmente una variedad diferenciable) que tome valores prescritos sobre el contorno de dicho dominio. El problema de Dirichlet puede resolverse para muchas EDPs, aunque originalmente fue planteada para la ecuaci\u00F3n de Laplace. En este caso el problema puede enunciarse como sigue:"@es . . "\u041C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u0414\u0456\u0440\u0456\u0445\u043B\u0435 \u0430\u0431\u043E \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u043F\u0435\u0440\u0448\u043E\u0433\u043E \u0440\u043E\u0434\u0443 \u2014 \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0430\u0431\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445, \u0432 \u044F\u043A\u0438\u0445 \u043D\u0430 \u043C\u0435\u0436\u0456 \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0454\u0442\u044C\u0441\u044F \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u043D\u0435\u0432\u0456\u0434\u043E\u043C\u043E\u0457 \u0444\u0443\u043D\u043A\u0446\u0456\u0457. \u0423 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u043C\u043E\u0436\u0443\u0442\u044C \u0437\u0430\u0434\u0430\u0432\u0430\u0442\u0438\u0441\u044F \u043D\u0430 \u044F\u043A\u043E\u043C\u0443\u0441\u044C \u0430\u0431\u043E \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456, \u0430 \u0442\u043E\u043C\u0443 \u043C\u043E\u0436\u0443\u0442\u044C \u0431\u0443\u0442\u0438 \u0444\u0443\u043D\u043A\u0446\u0456\u0454\u044E, \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043E\u043C\u0443 \u043D\u0430 \u0446\u044C\u043E\u043C\u0443 \u043A\u043E\u043D\u0442\u0443\u0440\u0456 \u0447\u0438 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . . . . . "\uC218\uD559\uC5D0\uC11C \uB514\uB9AC\uD074\uB808 \uBB38\uC81C(Dirichlet problem)\uB780 \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74\uC744 \uAC00\uC9C4 \uACBD\uACC4\uAC12 \uBB38\uC81C\uB2E4. \uC989, \uC8FC\uC5B4\uC9C4 \uC601\uC5ED\uC758 \uACBD\uACC4\uC5D0\uC11C\uC758 \uAC12\uC774 \uC870\uAC74\uC73C\uB85C \uC8FC\uC5B4\uC9C0\uB294 \uD2B9\uC815\uD55C \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC5D0 \uB300\uD558\uC5EC \uADF8 \uC601\uC5ED\uC758 \uB0B4\uBD80\uC5D0\uC11C\uC758 \uD574\uAC00 \uB420 \uC218 \uC788\uB294 \uD568\uC218\uB97C \uCC3E\uB294 \uBB38\uC81C\uC774\uB2E4. \uB514\uB9AC\uD074\uB808 \uBB38\uC81C\uB294 \uB9CE\uC740 \uC885\uB958\uC758 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uD480 \uC218 \uC788\uAC8C \uD558\uB294\uB370, \uC5ED\uC0AC\uC801\uC73C\uB85C \uB77C\uD50C\uB77C\uC2A4 \uBC29\uC815\uC2DD\uC744 \uD480\uC774\uD558\uAE30 \uC704\uD55C \uBC29\uBC95\uB860\uC73C\uB85C \uBC1C\uC804\uB418\uC5C8\uB2E4.\uC774\uB54C\uC758 \uC694\uAD6C\uB418\uB294 \uC870\uAC74\uC774 \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74\uC774\uB2E4. \uC8FC\uB85C \uD574\uC758 \uC874\uC7AC\uC131\uACFC \uC720\uC77C\uC131\uC774 \uC8FC\uC694\uD55C \uB17C\uC810\uC774 \uB418\uB294\uB370, \uC774\uAC83\uC740 \uCD5C\uB300 \uC6D0\uB9AC\uC5D0 \uC758\uD574 \uC99D\uBA85\uD560 \uC218 \uC788\uB2E4."@ko . "En matem\u00E1ticas, la condici\u00F3n de frontera de Dirichlet (o de primer tipo) es un tipo de condici\u00F3n de frontera o contorno, denominado as\u00ED en honor a Johann Peter Gustav Lejeune Dirichlet (1805-1859),\u200B cuando en una ecuaci\u00F3n diferencial ordinaria o una en derivadas parciales, se le especifican los valores de la soluci\u00F3n que necesita la frontera del dominio. La cuesti\u00F3n de hallar las soluciones a esas ecuaciones con esta condici\u00F3n se le conoce como problema de Dirichlet."@es . . "\u72C4\u5229\u514B\u96F7\u95EE\u9898"@zh . . . "Em matem\u00E1tica, a condi\u00E7\u00E3o de contorno de Dirichlet (ou de primeiro tipo) \u00E9 um tipo de condi\u00E7\u00E3o de contorno, nomeada em homenagem a Johann Peter Gustav Lejeune Dirichlet (1805-1859). Quando aplicada sobre uma equa\u00E7\u00E3o diferencial ordin\u00E1ria ou parcial, especifica os valores que uma solu\u00E7\u00E3o necessita tomar no contorno do dom\u00EDnio. A quest\u00E3o de encontrar-se solu\u00E7\u00F5es para tais equa\u00E7\u00F5es \u00E9 conhecida como problema de Dirichlet. No caso de uma equa\u00E7\u00E3o diferencial ordin\u00E1ria tal como: no intervalo [0,1] as condi\u00E7\u00F5es de contorno de Dirichlet tomam a forma: onde \u03B11 e \u03B12 s\u00E3o n\u00FAmeros dados."@pt . . . "p/d032910"@en . "\u30C7\u30A3\u30EA\u30AF\u30EC\u5883\u754C\u6761\u4EF6\uFF08\u30C7\u30A3\u30EA\u30AF\u30EC\u304D\u3087\u3046\u304B\u3044\u3058\u3087\u3046\u3051\u3093\uFF09\u3042\u308B\u3044\u306F\u7B2C1\u7A2E\u5883\u754C\u6761\u4EF6\u306F\u3001\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u304A\u3051\u308B\u5883\u754C\u6761\u4EF6\u306E\u4E00\u3064\u306E\u5F62\u72B6\u3067\u3042\u308A\u3001\u5883\u754C\u6761\u4EF6\u4E0A\u306E\u70B9\u306E\u5024\u3092\u76F4\u306B\u4E0E\u3048\u308B\u3082\u306E\u3067\u3042\u308B\u3002 \u3088\u308A\u53B3\u5BC6\u306B\u8A00\u3046\u3068\u3001y \u306B\u95A2\u3059\u308B\u5FAE\u5206\u65B9\u7A0B\u5F0F\u3067\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u5883\u754C\u4E0A\u306E\u70B9\u306E\u96C6\u5408\u3092 \u03A9 \u3068\u3057\u305F\u3068\u304D\u306B\u3001\u03A9 \u306B\u542B\u307E\u308C\u308B\u70B9 x \u304C\u3042\u308C\u3070 \u3068\u3044\u3046\u5F62\u3067\u8868\u73FE\u3067\u304D\u308B\u3088\u3046\u306A\u5883\u754C\u6761\u4EF6\u3067\u3042\u308B\u3002 \u4F8B\u3048\u3070\u3001\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F \u306B\u304A\u3044\u3066\u3001\u4E00\u822C\u89E3\u306F \u3068\u306A\u308B\u304C\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3068\u3057\u3066 y(0) = 1 \u3068\u3059\u308B\u3068\u3001 \u3068\u3044\u3046\u89E3\u304C\u5F97\u3089\u308C\u308B\u3002 \u306A\u304A\u3001\u4E00\u3064\u306E\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306B\u304A\u3044\u3066\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u4EE5\u5916\u306E\u5883\u754C\u6761\u4EF6\u3068\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3092\u4F75\u7528\u3057\u3066\u8A2D\u5B9A\u3059\u308B\u3053\u3068\u3082\u73CD\u3057\u304F\u306A\u3044\u3002\u305F\u3060\u3057\u3001\u5C11\u306A\u304F\u3068\u3082\u30C7\u30A3\u30EA\u30AF\u30EC\u6761\u4EF6\u3068\u540C\u7B49\u3068\u306A\u308B\u70B9\u304C1\u3064\u4EE5\u4E0A\u5B58\u5728\u3057\u306A\u3044\u5834\u5408\u306F\u3001\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u89E3\u304C\u6C7A\u5B9A\u3055\u308C\u306A\u3044\u3002"@ja . . . . . . "In matematica, una condizione al contorno di Dirichlet, il cui nome \u00E8 dovuto al matematico Peter Gustav Lejeune Dirichlet (1805\u20131859), \u00E8 una particolare condizione al contorno imposta in un'equazione differenziale, ordinaria o alle derivate parziali, che specifica i valori che la soluzione deve assumere su una superficie, per esempio ."@it . "\u0413\u0440\u0430\u043D\u0438\u0447\u043D\u0456 \u0443\u043C\u043E\u0432\u0438 \u0414\u0456\u0440\u0456\u0445\u043B\u0435"@uk . "d/d032910"@en . . . "En matem\u00E0tiques, la condici\u00F3 de contorn o condici\u00F3 de frontera de Dirichlet (o de primer tipus) \u00E9s un tipus de condici\u00F3 de frontera, que rep el nom de Peter Gustav Lejeune Dirichlet (1805\u20131859). Quan s'aplica a equacions diferencials ordin\u00E0ries o a equacions en derivades parcials, especifica el valor que ha de prendre la soluci\u00F3 en la frontera del domini. La resoluci\u00F3 d'aquest tipus d'equacions es coneix pel nom de problema de Dirichlet. En enginyeria, les condicions de contorn de Dirichlet tamb\u00E9 s\u00F3n conegudes com a condicions de contorn fixes."@ca . . . . "Problem Dirichleta polega na znalezieniu funkcji harmonicznej dla danego obszaru z danymi warto\u015Bciami na brzegu. Problem ten zosta\u0142 po raz pierwszy postawiony przez Lejeune\u2019a Dirichleta dla r\u00F3wnania Laplace\u2019a."@pl . "Problema de Dirichlet"@ca . "Condi\u00E7\u00E3o de contorno de Dirichlet"@pt . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0456\u0440\u0456\u0445\u043B\u0435 \u2014 \u0432\u0438\u0434 \u0437\u0430\u0434\u0430\u0447, \u0449\u043E \u0437'\u044F\u0432\u043B\u044F\u0454\u0442\u044C\u0441\u044F \u043F\u0440\u0438 \u0440\u043E\u0437\u0432'\u044F\u0437\u0430\u043D\u043D\u0456 \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0437 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u043C\u0438 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u043C\u0438 \u0434\u0440\u0443\u0433\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0443. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0419\u043E\u0433\u0430\u043D\u043D\u0430 \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . "In matematica, un problema di Dirichlet richiede di trovare una funzione che soddisfa una determinata equazione differenziale alle derivate parziali (PDE) all'interno di una regione sulla cui frontiera la funzione assume determinati valori al contorno. In origine il problema fu introdotto specificatamente per l'equazione di Laplace, ma pu\u00F2 essere posto per molte PDE."@it . "\uB514\uB9AC\uD074\uB808 \uBB38\uC81C"@ko . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0438\u0440\u0438\u0445\u043B\u0435 \u2014 \u0432\u0438\u0434 \u0437\u0430\u0434\u0430\u0447, \u043F\u043E\u044F\u0432\u043B\u044F\u044E\u0449\u0438\u0439\u0441\u044F \u043F\u0440\u0438 \u0440\u0435\u0448\u0435\u043D\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u0432\u0442\u043E\u0440\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u041F\u0435\u0442\u0435\u0440\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u0414\u0438\u0440\u0438\u0445\u043B\u0435."@ru . . . . "Problema di Dirichlet"@it . . "Problem Dirichleta"@pl . . "Condici\u00F3 de frontera de Dirichlet"@ca . . . "\u0413\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0414\u0438\u0440\u0438\u0445\u043B\u0435 (\u0433\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u0440\u043E\u0434\u0430) \u2014 \u0442\u0438\u043F \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0445 \u0443\u0441\u043B\u043E\u0432\u0438\u0439, \u043D\u0430\u0437\u0432\u0430\u043D\u043D\u044B\u0439 \u0432 \u0447\u0435\u0441\u0442\u044C \u043D\u0435\u043C\u0435\u0446\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041F. \u0413. \u0414\u0438\u0440\u0438\u0445\u043B\u0435. \u0423\u0441\u043B\u043E\u0432\u0438\u0435 \u0414\u0438\u0440\u0438\u0445\u043B\u0435, \u043F\u0440\u0438\u043C\u0435\u043D\u0451\u043D\u043D\u043E\u0435 \u043A \u043E\u0431\u044B\u043A\u043D\u043E\u0432\u0435\u043D\u043D\u044B\u043C \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C \u0438\u043B\u0438 \u043A \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445, \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u043D\u0430 \u0433\u0440\u0430\u043D\u0438\u0446\u0435 \u043E\u0431\u043B\u0430\u0441\u0442\u0438. \u0417\u0430\u0434\u0430\u0447\u0430 \u043E \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u0438 \u0442\u0430\u043A\u0438\u0445 \u0443\u0441\u043B\u043E\u0432\u0438\u0439 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0437\u0430\u0434\u0430\u0447\u0435\u0439 \u0414\u0438\u0440\u0438\u0445\u043B\u0435."@ru . . "En math\u00E9matiques, une condition aux limites de Dirichlet (nomm\u00E9e d\u2019apr\u00E8s Johann Dirichlet) est impos\u00E9e \u00E0 une \u00E9quation diff\u00E9rentielle ou \u00E0 une \u00E9quation aux d\u00E9riv\u00E9es partielles lorsque l'on sp\u00E9cifie les valeurs que la solution doit v\u00E9rifier sur les fronti\u00E8res/limites du domaine. \n* Pour une \u00E9quation diff\u00E9rentielle, par exemple : la condition aux limites de Dirichlet sur l'intervalle s'exprime par : o\u00F9 et sont deux nombres donn\u00E9s. \n* Pour une \u00E9quation aux d\u00E9riv\u00E9es partielles, par exemple : o\u00F9 est une fonction connue d\u00E9finie sur la fronti\u00E8re ."@fr . "\u5728\u6570\u5B66\u4E2D\uFF0C\u72C4\u5229\u514B\u96F7\u8FB9\u754C\u6761\u4EF6\uFF08Dirichlet boundary condition\uFF09\u4E5F\u88AB\u79F0\u4E3A\u5E38\u5FAE\u5206\u65B9\u7A0B\u6216\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u201C\u7B2C\u4E00\u7C7B\u8FB9\u754C\u6761\u4EF6\u201D\uFF0C\u6307\u5B9A\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u5728\u8FB9\u754C\u5904\u7684\u503C\u3002\u6C42\u51FA\u8FD9\u6837\u7684\u65B9\u7A0B\u7684\u89E3\u7684\u95EE\u9898\u88AB\u79F0\u4E3A\u72C4\u5229\u514B\u96F7\u95EE\u9898\u3002"@zh . . "\u041C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u0414\u0456\u0440\u0456\u0445\u043B\u0435 \u0430\u0431\u043E \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u043F\u0435\u0440\u0448\u043E\u0433\u043E \u0440\u043E\u0434\u0443 \u2014 \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0430\u0431\u043E \u0434\u0438\u0444\u0435\u0440\u0435\u043D\u0446\u0456\u0439\u043D\u043E\u0433\u043E \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445, \u0432 \u044F\u043A\u0438\u0445 \u043D\u0430 \u043C\u0435\u0436\u0456 \u0432\u0438\u0437\u043D\u0430\u0447\u0430\u0454\u0442\u044C\u0441\u044F \u0437\u043D\u0430\u0447\u0435\u043D\u043D\u044F \u043D\u0435\u0432\u0456\u0434\u043E\u043C\u043E\u0457 \u0444\u0443\u043D\u043A\u0446\u0456\u0457. \u0423 \u0432\u0438\u043F\u0430\u0434\u043A\u0443 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0432 \u0447\u0430\u0441\u0442\u043A\u043E\u0432\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u043C\u0435\u0436\u043E\u0432\u0456 \u0443\u043C\u043E\u0432\u0438 \u043C\u043E\u0436\u0443\u0442\u044C \u0437\u0430\u0434\u0430\u0432\u0430\u0442\u0438\u0441\u044F \u043D\u0430 \u044F\u043A\u043E\u043C\u0443\u0441\u044C \u0430\u0431\u043E \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456, \u0430 \u0442\u043E\u043C\u0443 \u043C\u043E\u0436\u0443\u0442\u044C \u0431\u0443\u0442\u0438 \u0444\u0443\u043D\u043A\u0446\u0456\u0454\u044E, \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043E\u043C\u0443 \u043D\u0430 \u0446\u044C\u043E\u043C\u0443 \u043A\u043E\u043D\u0442\u0443\u0440\u0456 \u0447\u0438 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456. \u041D\u0430\u0437\u0432\u0430\u043D\u0456 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0414\u0456\u0440\u0456\u0445\u043B\u0435."@uk . . "En math\u00E9matiques, une condition aux limites de Dirichlet (nomm\u00E9e d\u2019apr\u00E8s Johann Dirichlet) est impos\u00E9e \u00E0 une \u00E9quation diff\u00E9rentielle ou \u00E0 une \u00E9quation aux d\u00E9riv\u00E9es partielles lorsque l'on sp\u00E9cifie les valeurs que la solution doit v\u00E9rifier sur les fronti\u00E8res/limites du domaine. \n* Pour une \u00E9quation diff\u00E9rentielle, par exemple : la condition aux limites de Dirichlet sur l'intervalle s'exprime par : o\u00F9 et sont deux nombres donn\u00E9s. \n* Pour une \u00E9quation aux d\u00E9riv\u00E9es partielles, par exemple : o\u00F9 est le Laplacien (op\u00E9rateur diff\u00E9rentiel), la condition aux limites de Dirichlet sur un domaine s'exprime par : o\u00F9 est une fonction connue d\u00E9finie sur la fronti\u00E8re . Il existe d'autres conditions possibles. Par exemple la condition aux limites de Neumann, ou la condition aux limites de Robin, qui est une combinaison des conditions de Dirichlet et Neumann."@fr . . . . . . "En matem\u00E1ticas, la condici\u00F3n de frontera de Dirichlet (o de primer tipo) es un tipo de condici\u00F3n de frontera o contorno, denominado as\u00ED en honor a Johann Peter Gustav Lejeune Dirichlet (1805-1859),\u200B cuando en una ecuaci\u00F3n diferencial ordinaria o una en derivadas parciales, se le especifican los valores de la soluci\u00F3n que necesita la frontera del dominio. La cuesti\u00F3n de hallar las soluciones a esas ecuaciones con esta condici\u00F3n se le conoce como problema de Dirichlet."@es . "\u72C4\u5229\u514B\u96F7\u8FB9\u754C\u6761\u4EF6"@zh . . "In matematica, una condizione al contorno di Dirichlet, il cui nome \u00E8 dovuto al matematico Peter Gustav Lejeune Dirichlet (1805\u20131859), \u00E8 una particolare condizione al contorno imposta in un'equazione differenziale, ordinaria o alle derivate parziali, che specifica i valori che la soluzione deve assumere su una superficie, per esempio ."@it . . . . . "\uC218\uD559\uC5D0\uC11C \uB514\uB9AC\uD074\uB808 \uACBD\uACC4 \uC870\uAC74(Dirichlet boundary condition)\uC740 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uC758 \uC911\uC758 \uD558\uB098\uC774\uBA70, \uACBD\uACC4\uC5D0\uC11C \uC810\uC758 \uAC12\uC744 \uC9C1\uC811 \uC8FC\uB294 \uAC83\uC774\uB2E4. \uC218\uD559\uC790 \uD398\uD130 \uAD6C\uC2A4\uD0C0\uD504 \uB974\uC8C8 \uB514\uB9AC\uD074\uB808\uC758 \uC774\uB984\uC744 \uB530\uACE0 \uC788\uB2E4."@ko . "571109"^^ . . "En math\u00E9matiques, le probl\u00E8me de Dirichlet est de trouver une fonction harmonique d\u00E9finie sur un ouvert de prolongeant une fonction continue d\u00E9finie sur la fronti\u00E8re de l'ouvert . Ce probl\u00E8me porte le nom du math\u00E9maticien allemand Johann Peter Gustav Lejeune Dirichlet."@fr . "DirichletProblem"@en . . . . "\u30C7\u30A3\u30EA\u30AF\u30EC\u554F\u984C"@ja . . . "Condition aux limites de Dirichlet"@fr . . "En matem\u00E0tiques, la condici\u00F3 de contorn o condici\u00F3 de frontera de Dirichlet (o de primer tipus) \u00E9s un tipus de condici\u00F3 de frontera, que rep el nom de Peter Gustav Lejeune Dirichlet (1805\u20131859). Quan s'aplica a equacions diferencials ordin\u00E0ries o a equacions en derivades parcials, especifica el valor que ha de prendre la soluci\u00F3 en la frontera del domini. La resoluci\u00F3 d'aquest tipus d'equacions es coneix pel nom de problema de Dirichlet. En enginyeria, les condicions de contorn de Dirichlet tamb\u00E9 s\u00F3n conegudes com a condicions de contorn fixes."@ca . . . "In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally it was posed for Laplace's equation. In that case the problem can be stated as follows: Given a function f that has values everywhere on the boundary of a region in Rn, is there a unique continuous function u twice continuously differentiable in the interior and continuous on the boundary, such that u is harmonic in the interior and u = f on the boundary? This requirement is called the Dirichlet boundary condition. The main issue is to prove the existence of a solution; uniqueness can be proved using the maximum principle."@en . . "\u0413\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u0414\u0438\u0440\u0438\u0445\u043B\u0435 (\u0433\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0435 \u0443\u0441\u043B\u043E\u0432\u0438\u044F \u043F\u0435\u0440\u0432\u043E\u0433\u043E \u0440\u043E\u0434\u0430) \u2014 \u0442\u0438\u043F \u0433\u0440\u0430\u043D\u0438\u0447\u043D\u044B\u0445 \u0443\u0441\u043B\u043E\u0432\u0438\u0439, \u043D\u0430\u0437\u0432\u0430\u043D\u043D\u044B\u0439 \u0432 \u0447\u0435\u0441\u0442\u044C \u043D\u0435\u043C\u0435\u0446\u043A\u043E\u0433\u043E \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041F. \u0413. \u0414\u0438\u0440\u0438\u0445\u043B\u0435. \u0423\u0441\u043B\u043E\u0432\u0438\u0435 \u0414\u0438\u0440\u0438\u0445\u043B\u0435, \u043F\u0440\u0438\u043C\u0435\u043D\u0451\u043D\u043D\u043E\u0435 \u043A \u043E\u0431\u044B\u043A\u043D\u043E\u0432\u0435\u043D\u043D\u044B\u043C \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C \u0438\u043B\u0438 \u043A \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445, \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u044F\u0435\u0442 \u043F\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043C\u044B \u043D\u0430 \u0433\u0440\u0430\u043D\u0438\u0446\u0435 \u043E\u0431\u043B\u0430\u0441\u0442\u0438. \u0417\u0430\u0434\u0430\u0447\u0430 \u043E \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u0438 \u0442\u0430\u043A\u0438\u0445 \u0443\u0441\u043B\u043E\u0432\u0438\u0439 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0437\u0430\u0434\u0430\u0447\u0435\u0439 \u0414\u0438\u0440\u0438\u0445\u043B\u0435."@ru . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0438\u0440\u0438\u0445\u043B\u0435"@ru . . . "Dirichletvillkor"@sv . . "Dirichlet problem"@en . . . . . . "Dirichlet problem"@en . . "Dirichletvillkor \u00E4r en typ av randvillkor f\u00F6r differentialekvationer d\u00E4r l\u00F6sningen f\u00F6reskrivs ha ett fixt givet v\u00E4rde p\u00E5 randen eller en del av denna."@sv . . . . "Em matem\u00E1tica, a condi\u00E7\u00E3o de contorno de Dirichlet (ou de primeiro tipo) \u00E9 um tipo de condi\u00E7\u00E3o de contorno, nomeada em homenagem a Johann Peter Gustav Lejeune Dirichlet (1805-1859). Quando aplicada sobre uma equa\u00E7\u00E3o diferencial ordin\u00E1ria ou parcial, especifica os valores que uma solu\u00E7\u00E3o necessita tomar no contorno do dom\u00EDnio. A quest\u00E3o de encontrar-se solu\u00E7\u00F5es para tais equa\u00E7\u00F5es \u00E9 conhecida como problema de Dirichlet. No caso de uma equa\u00E7\u00E3o diferencial ordin\u00E1ria tal como: no intervalo [0,1] as condi\u00E7\u00F5es de contorno de Dirichlet tomam a forma: onde \u03B11 e \u03B12 s\u00E3o n\u00FAmeros dados. Para uma equa\u00E7\u00E3o diferencial parcial num dom\u00EDnio \u03A9\u2282\u211D\u207F tal como: onde denota o Laplaciano, a condi\u00E7\u00E3o de contorno de Dirichlet toma a forma: onde f \u00E9 uma fun\u00E7\u00E3o conhecida definida no contorno \u2202\u03A9. Condi\u00E7\u00F5es de contorno de Dirichlet s\u00E3o talvez as mais f\u00E1ceis de serem entendidas, mas existem muitas outras condi\u00E7\u00F5es poss\u00EDveis. Por exemplo, h\u00E1 a ou condi\u00E7\u00E3o de contorno mista que \u00E9 uma combina\u00E7\u00E3o das condi\u00E7\u00F5es de Dirichlet e Neumann."@pt . "Em matem\u00E1tica, um problema de Dirichlet consiste em encontrar uma fun\u00E7\u00E3o que satisfa\u00E7a uma equa\u00E7\u00E3o diferencial parcial (EDP) dada no interior de uma regi\u00E3o dada e que toma valores prescritos na fronteira (contorno) desta. Originalmente, o problema foi proposto para a equa\u00E7\u00E3o de Laplace. Nesse caso ele pode ser apresentado da seguinte forma: dada uma fun\u00E7\u00E3o definida no contorno de um dado conjunto em Rn, existe uma \u00FAnica fun\u00E7\u00E3o cont\u00EDnua u diferenci\u00E1vel continuamente duas vezes no interior e cont\u00EDnua no contorno, tal que \u00E9 harm\u00F4nica no interior e no contorno?"@pt . "Als Dirichlet-Randbedingung (nach Peter Gustav Lejeune Dirichlet) bezeichnet man im Zusammenhang mit Differentialgleichungen (genauer: Randwertproblemen) Werte, die auf dem jeweiligen Rand des Definitionsbereichs von der Funktion angenommen werden sollen. Weitere Randbedingungen sind beispielsweise Neumann-Randbedingungen oder schiefe Randbedingungen."@de . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0438\u0440\u0438\u0445\u043B\u0435 \u2014 \u0432\u0438\u0434 \u0437\u0430\u0434\u0430\u0447, \u043F\u043E\u044F\u0432\u043B\u044F\u044E\u0449\u0438\u0439\u0441\u044F \u043F\u0440\u0438 \u0440\u0435\u0448\u0435\u043D\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u0445 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u0439 \u0432 \u0447\u0430\u0441\u0442\u043D\u044B\u0445 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u0445 \u0432\u0442\u043E\u0440\u043E\u0433\u043E \u043F\u043E\u0440\u044F\u0434\u043A\u0430. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u041F\u0435\u0442\u0435\u0440\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u0414\u0438\u0440\u0438\u0445\u043B\u0435."@ru . . "\u30C7\u30A3\u30EA\u30AF\u30EC\u554F\u984C\uFF08\u82F1\u8A9E: Dirichlet problem\uFF09\u3068\u306F\u3001\u30E9\u30D7\u30E9\u30B9\u65B9\u7A0B\u5F0F\u3092\u3042\u308B\u9818\u57DF \u03A9 \u3067\u3001\u5883\u754C\u4E0A\u3067 \u03C6=G \u3068\u3044\u3046\u6761\u4EF6\u3067\u89E3\u3068\u306A\u308B\u8ABF\u548C\u95A2\u6570 \u03C6 = \u03C6(x1, x2, ..., xn) \u3092\u6C42\u3081\u308B\u554F\u984C\u3067\u3042\u308B\u3002\u7B2C\u4E00\u5883\u754C\u5024\u554F\u984C\u3068\u3082\u547C\u3070\u308C\u308B\u3002\u89E3\u6CD5\u306B\u306F\u3001\u30B0\u30EA\u30FC\u30F3\u95A2\u6570\u3001\u30C7\u30A3\u30EA\u30AF\u30EC\u306E\u539F\u7406\u3001\u4EA4\u4EE3\u6CD5\u3001\u30DD\u30A2\u30F3\u30AB\u30EC\u306E\u6383\u6563\u6CD5\u3001\u30DA\u30ED\u30F3\u6CD5\u306A\u3069\u304C\u3042\u308B\u3002"@ja . "\u0417\u0430\u0434\u0430\u0447\u0430 \u0414\u0456\u0440\u0456\u0445\u043B\u0435"@uk . . . . . "En matem\u00E0tiques, el problema de Dirichlet consisteix a trobar una funci\u00F3 que resolgui una equaci\u00F3 diferencial parcial a l'interior d'una donada que t\u00E9 valors predeterminats al contorn de la regi\u00F3. Les condicions de frontera d'aquest problema s'anomenen Condicions de frontera de Dirichlet. El problema de Dirichlet es pot resoldre per moltes equacions diferencials parcials, tot i que en un primer moment va ser pensat per a l'equaci\u00F3 de Laplace. En aquest cas el problema es pot formular de la manera seg\u00FCent: Aquest requeriment s'anomena la condici\u00F3 de contorn de Dirichlet."@ca . . . . "13564"^^ . . . "Warunek brzegowy Dirichleta \u2013 typ warunku brzegowego, znany tak\u017Ce jako warunek pierwszego rodzaju, u\u017Cywanym w teorii r\u00F3wna\u0144 r\u00F3\u017Cniczkowych zwyczajnych lub cz\u0105stkowych. Polega on na za\u0142o\u017Ceniu, \u017Ce funkcja b\u0119d\u0105ca rozwi\u0105zaniem danego problemu musi przyjmowa\u0107 okre\u015Blone, z g\u00F3ry zadane warto\u015Bci na brzegu dziedziny. Nazwa pochodzi od matematyka P. Dirichleta (1805\u20131859). Je\u017Celi dla r\u00F3wnania r\u00F3\u017Cniczkowego (zwyczajnego lub cz\u0105stkowego) stawiamy warunek brzegowy Dirichleta (na ca\u0142ym brzegu), to m\u00F3wimy o zagadnieniu (problemie) Dirichleta."@pl . . . "Dirichletvillkor \u00E4r en typ av randvillkor f\u00F6r differentialekvationer d\u00E4r l\u00F6sningen f\u00F6reskrivs ha ett fixt givet v\u00E4rde p\u00E5 randen eller en del av denna."@sv . . . . . "Problema de Dirichlet"@es . "En math\u00E9matiques, le probl\u00E8me de Dirichlet est de trouver une fonction harmonique d\u00E9finie sur un ouvert de prolongeant une fonction continue d\u00E9finie sur la fronti\u00E8re de l'ouvert . Ce probl\u00E8me porte le nom du math\u00E9maticien allemand Johann Peter Gustav Lejeune Dirichlet."@fr . "Em matem\u00E1tica, um problema de Dirichlet consiste em encontrar uma fun\u00E7\u00E3o que satisfa\u00E7a uma equa\u00E7\u00E3o diferencial parcial (EDP) dada no interior de uma regi\u00E3o dada e que toma valores prescritos na fronteira (contorno) desta. Originalmente, o problema foi proposto para a equa\u00E7\u00E3o de Laplace. Nesse caso ele pode ser apresentado da seguinte forma: dada uma fun\u00E7\u00E3o definida no contorno de um dado conjunto em Rn, existe uma \u00FAnica fun\u00E7\u00E3o cont\u00EDnua u diferenci\u00E1vel continuamente duas vezes no interior e cont\u00EDnua no contorno, tal que \u00E9 harm\u00F4nica no interior e no contorno? A exig\u00EAncia imposta sobre na fronteira do conjunto \u00E9 chamada de condi\u00E7\u00E3o de contorno de Dirichlet. A quest\u00E3o principal \u00E9 provar a exist\u00EAncia de uma solu\u00E7\u00E3o. A unicidade pode ser demonstrada usando-se o princ\u00EDpio do m\u00E1ximo."@pt . .