Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations

DOI10.1080/03605302.2010.514171zbMath1232.35076OpenAlexW2057084916MaRDI QIDQ3104528

Weiye Wang, Genggeng Huang, Jia-Xing Hong

Publication date: 14 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2010.514171

zbMATH Keywords

Monge-Ampère equationsglobal smooth solutionsdegenerate ellipticity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

Related Items (11)

Curvature estimates for the level sets of solutions to a class of Monge-Ampère equations ⋮ Local solvability of the \(k\)-Hessian equations ⋮ Compactness of Alexandrov‐Nirenberg Surfaces ⋮ Analyticity of the solutions to degenerate Monge-Ampère equations ⋮ The Guillemin boundary problem for Monge-Ampère equation in the polygon ⋮ Uniqueness of Nontrivial Solutions for Degenerate Monge–Ampere Equations ⋮ \(C^{1,1}\) solution of the Dirichlet problem for degenerate \(k\)-Hessian equations ⋮ Curvature estimates for the level sets of solutions to the Monge-Ampère equation \(\mathrm{det}D^{2}u = 1\) ⋮ Uniqueness of least energy solutions for Monge-Ampère functional ⋮ Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions ⋮ Regularity of the homogeneous Monge-Ampère equation

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