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- Monge–Ampère_equation abstract "Not be confused with the unconnected Monge equation.In mathematics, a (real) Monge–Ampère equation is a nonlinear second order partial differential equation of special kind. A second order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.Monge–Ampère equations frequently arise in differential geometry, for example, in the Weyl and Minkowski problems in differential geometry of surfaces. They were first studied by Gaspard Monge in 1784 and later by André-Marie Ampère in 1820. Important results in the theory of Monge–Ampère equations have been obtained by Sergei Bernstein, Aleksei Pogorelov, Charles Fefferman, and Louis Nirenberg.".
- Monge–Ampère_equation wikiPageID "4914066".
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- Monge–Ampère_equation wikiPageOutDegree "31".
- Monge–Ampère_equation wikiPageRevisionID "617438485".
- Monge–Ampère_equation wikiPageWikiLink Aleksei_Pogorelov.
- Monge–Ampère_equation wikiPageWikiLink André-Marie_Ampère.
- Monge–Ampère_equation wikiPageWikiLink CR_geometry.
- Monge–Ampère_equation wikiPageWikiLink CR_manifold.
- Monge–Ampère_equation wikiPageWikiLink Calabi_conjecture.
- Monge–Ampère_equation wikiPageWikiLink Category:Partial_differential_equations.
- Monge–Ampère_equation wikiPageWikiLink Charles_Fefferman.
- Monge–Ampère_equation wikiPageWikiLink Conformal_geometry.
- Monge–Ampère_equation wikiPageWikiLink Convex_function.
- Monge–Ampère_equation wikiPageWikiLink Determinant.
- Monge–Ampère_equation wikiPageWikiLink Differential_geometry.
- Monge–Ampère_equation wikiPageWikiLink Differential_geometry_of_surfaces.
- Monge–Ampère_equation wikiPageWikiLink Dirichlet_problem.
- Monge–Ampère_equation wikiPageWikiLink Elliptic_operator.
- Monge–Ampère_equation wikiPageWikiLink Elliptic_partial_differential_equation.
- Monge–Ampère_equation wikiPageWikiLink Gaspard_Monge.
- Monge–Ampère_equation wikiPageWikiLink Gauss_curvature.
- Monge–Ampère_equation wikiPageWikiLink Gaussian_curvature.
- Monge–Ampère_equation wikiPageWikiLink Hermann_Minkowski.
- Monge–Ampère_equation wikiPageWikiLink Hermann_Weyl.
- Monge–Ampère_equation wikiPageWikiLink Hessian_matrix.
- Monge–Ampère_equation wikiPageWikiLink Linearization.
- Monge–Ampère_equation wikiPageWikiLink Louis_Nirenberg.
- Monge–Ampère_equation wikiPageWikiLink Mathematics.
- Monge–Ampère_equation wikiPageWikiLink Maximum_principle.
- Monge–Ampère_equation wikiPageWikiLink Monge_equation.
- Monge–Ampère_equation wikiPageWikiLink Neil_Trudinger.
- Monge–Ampère_equation wikiPageWikiLink Nonlinear_equation.
- Monge–Ampère_equation wikiPageWikiLink Nonlinear_system.
- Monge–Ampère_equation wikiPageWikiLink Partial_derivative.
- Monge–Ampère_equation wikiPageWikiLink Partial_differential_equation.
- Monge–Ampère_equation wikiPageWikiLink Riemannian_geometry.
- Monge–Ampère_equation wikiPageWikiLink Sergei_Bernstein.
- Monge–Ampère_equation wikiPageWikiLink Sergei_Natanovich_Bernstein.
- Monge–Ampère_equation wikiPageWikiLink Transportation_theory_(mathematics).
- Monge–Ampère_equation wikiPageWikiLinkText "Monge–Ampere".
- Monge–Ampère_equation wikiPageWikiLinkText "Monge-Ampère".
- Monge–Ampère_equation wikiPageWikiLinkText "Monge–Ampère equation".
- Monge–Ampère_equation wikiPageWikiLinkText "Monge–Ampère operator".
- Monge–Ampère_equation wikiPageWikiLinkText "Monge–Ampère".
- Monge–Ampère_equation author "A.V. Pogorelov".
- Monge–Ampère_equation hasPhotoCollection Monge–Ampère_equation.
- Monge–Ampère_equation id "M/m064620".
- Monge–Ampère_equation title "Monge-Ampère Differential Equation".
- Monge–Ampère_equation title "Monge–Ampère equation".
- Monge–Ampère_equation urlname "Monge-AmpereDifferentialEquation".
- Monge–Ampère_equation wikiPageUsesTemplate Template:Cn.
- Monge–Ampère_equation wikiPageUsesTemplate Template:Mathworld.
- Monge–Ampère_equation wikiPageUsesTemplate Template:Springer.
- Monge–Ampère_equation subject Category:Partial_differential_equations.
- Monge–Ampère_equation comment "Not be confused with the unconnected Monge equation.In mathematics, a (real) Monge–Ampère equation is a nonlinear second order partial differential equation of special kind. A second order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2.".
- Monge–Ampère_equation label "Monge–Ampère equation".
- Monge–Ampère_equation sameAs Monge-Ampèresche_Gleichung.
- Monge–Ampère_equation sameAs m.0ctyfc.
- Monge–Ampère_equation sameAs Уравнение_Монжа_—_Ампера.
- Monge–Ampère_equation sameAs Q1552291.
- Monge–Ampère_equation sameAs Q1552291.
- Monge–Ampère_equation sameAs 齐次蒙日-安培方程.
- Monge–Ampère_equation wasDerivedFrom Monge–Ampère_equation?oldid=617438485.
- Monge–Ampère_equation isPrimaryTopicOf Monge–Ampère_equation.