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About: Monge equation     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatPartialDifferentialEquationsyago:Abstraction100002137yago:Communication100033020yago:DifferentialEquation106670521yago:Equation106669864yago:MathematicalStatement106732169yago:Message106598915yago:PartialDifferentialEquation106670866yago:Statement106722453 New Facet based on Instances of this Class

In the mathematical theory of partial differential equations, a Monge equation, named after Gaspard Monge, is a first-order partial differential equation for an unknown function u in the independent variables x1,...,xn that is a polynomial in the partial derivatives of u. Any Monge equation has a Monge cone. Classically, putting u = x0, a Monge equation of degree k is written in the form and expresses a relation between the differentials dxk. The Monge cone at a given point (x0, ..., xn) is the zero locus of the equation in the tangent space at the point.