About: Browder–Minty theorem

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In mathematics, the Browder–Minty theorem (sometimes called the Minty–Browder theorem) states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each continuous linear functional g ∈ X∗, there exists a solution u ∈ X of the equation T(u) = g. (Note that T itself is not required to be a linear map.) The theorem is named in honor of Felix Browder and George J. Minty, who independently proved it.

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rdfs:label	Satz von Minty-Browder (de) Browder–Minty theorem (en) Théorème de Browder-Minty (fr)
rdfs:comment	In mathematics, the Browder–Minty theorem (sometimes called the Minty–Browder theorem) states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each continuous linear functional g ∈ X∗, there exists a solution u ∈ X of the equation T(u) = g. (Note that T itself is not required to be a linear map.) The theorem is named in honor of Felix Browder and George J. Minty, who independently proved it. (en) En mathématiques, et plus précisément en analyse fonctionnelle, le théorème de Browder-Minty (ou Minty-Browder) est une généralisation, pour les opérateurs non linéaires, du théorème de Lax-Milgram.Il est démontré indépendamment en 1963 par Felix Browder et (de). Il intervient dans la démonstration de l'existence de solutions d'équations aux dérivées partielles non linéaires avec des conditions aux limites. (fr) Der Satz von Minty-Browder oder auch Satz von Browder und Minty, englisch Minty-Browder theorem, ist ein mathematischer Lehrsatz der Nichtlinearen Funktionalanalysis. Er geht auf Arbeiten der beiden Mathematiker George Minty und Felix Browder aus den Jahren 1962 und 1963 zurück. (de)
dcterms:subject	Banach spaces Operator theory Theorems in functional analysis
Wikipage page ID	11908534 (xsd:integer)
Wikipage revision ID	1027223136 (xsd:integer)
Link from a Wikipage to another Wikipage	Bounded function Banach spaces Pseudo-monotone operator Operator theory Continuous dual space Continuous function Continuous linear functional Theorems in functional analysis Mathematics Separable space Banach space Linear map Felix Browder Surjective Coercive function George J. Minty Real number Reflexive space Monotone function
sameAs	Browder–Minty theorem Browder–Minty theorem Browder–Minty theorem Browder–Minty theorem Browder–Minty theorem
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has abstract	Der Satz von Minty-Browder oder auch Satz von Browder und Minty, englisch Minty-Browder theorem, ist ein mathematischer Lehrsatz der Nichtlinearen Funktionalanalysis. Er geht auf Arbeiten der beiden Mathematiker George Minty und Felix Browder aus den Jahren 1962 und 1963 zurück. Der Satz behandelt die Frage der Bedingungen, unter denen ein monotoner Operator auf einem separablen reflexiven Banachraum über dem Körper der reellen Zahlen surjektiv ist. Er wird auch als Hauptsatz der Theorie monotoner Operatoren bezeichnet und gilt als nichtlineares Analogon zum Satz von Lax-Milgram. Der Satz findet vielfache Anwendung bei der Lösung nichtlinearer Randwertaufgaben der Variationsrechnung. Der Beweis des Satzes beruht auf dem Fixpunktsatz von Brouwer und der Galerkin-Methode. (de) In mathematics, the Browder–Minty theorem (sometimes called the Minty–Browder theorem) states that a bounded, continuous, coercive and monotone function T from a real, separable reflexive Banach space X into its continuous dual space X∗ is automatically surjective. That is, for each continuous linear functional g ∈ X∗, there exists a solution u ∈ X of the equation T(u) = g. (Note that T itself is not required to be a linear map.) The theorem is named in honor of Felix Browder and George J. Minty, who independently proved it. (en) En mathématiques, et plus précisément en analyse fonctionnelle, le théorème de Browder-Minty (ou Minty-Browder) est une généralisation, pour les opérateurs non linéaires, du théorème de Lax-Milgram.Il est démontré indépendamment en 1963 par Felix Browder et (de). Il intervient dans la démonstration de l'existence de solutions d'équations aux dérivées partielles non linéaires avec des conditions aux limites. (fr)
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is Link from a Wikipage to another Wikipage of	Pseudo-monotone operator Browder-Minty theorem Logarithmic norm Felix Browder George J. Minty List of theorems
is Wikipage redirect of	Browder-Minty theorem
is known for of	Felix Browder
is known for of	Felix Browder
is foaf:primaryTopic of	wikipedia-en:Browder–Minty_theorem

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