Existence and nonexistence to exterior Dirichlet problem for Monge-Ampère equation

DOI10.1007/s00526-018-1428-5zbMath1402.53031arXiv1804.00239OpenAlexW2963124440WikidataQ115387218 ScholiaQ115387218MaRDI QIDQ1787139

Yanyan Li

Publication date: 4 October 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.00239

zbMATH Keywords

Monge-Ampère equationexterior Dirichlet problem

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (14)

The exterior Dirichlet problems of Monge-Ampère equations in dimension two ⋮ The first initial-boundary value problem of parabolic Monge-Ampère equations outside a bowl-shaped domain ⋮ Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior ⋮ Necessary and sufficient conditions on the existence of solutions for the exterior Dirichlet problem of Hessian equations ⋮ Existence and uniqueness of viscosity solutions to the exterior problem of a parabolic Monge-Ampère equation ⋮ The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations ⋮ Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase ⋮ Symmetry of solutions of minimal gradient graph equations on punctured space ⋮ On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations ⋮ Boundary blow-up solutions to the Monge-Ampère equation: sharp conditions and asymptotic behavior ⋮ Ancient solutions of exterior problem of parabolic Monge-Ampère equations ⋮ Blow-up solutions to the Monge-Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates ⋮ A class of singular coupled systems of superlinear Monge-Ampère equations ⋮ Existence of entire solutions of Monge-Ampère equations with prescribed asymptotic behavior

Cites Work

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• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
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• Some aspects of the global geometry of entire space-like submanifolds

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