Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions

DOI10.1007/S00222-016-0677-1zbMath1361.35066arXiv1504.00912OpenAlexW2963604726MaRDI QIDQ504142

Nam Q. Le, Ovidiu V. Savin

Publication date: 25 January 2017

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00912

zbMATH Keywords

Monge-Ampère equationSchauder estimates

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Monge-Ampère equations (35J96)

Related Items (19)

Solvability of a class of singular fourth order equations of Monge-Ampère type ⋮ Boundary Hölder estimates for nonlinear singular elliptic equations ⋮ On the regularity of optimal transports between degenerate densities ⋮ Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions ⋮ On parabolic and elliptic equations with singular or degenerate coefficients ⋮ 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 ⋮ Boundary regularity for \(k\)-Hessian equations ⋮ Sharp boundary regularity for some degenerate-singular Monge-Ampère equations on \(k\)-convex domain ⋮ Unnamed Item ⋮ Regularity for parabolic equations with singular or degenerate coefficients ⋮ Uniqueness of least energy solutions for Monge-Ampère functional ⋮ Boundary blow-up solutions to a class of degenerate elliptic equations ⋮ Unnamed Item ⋮ Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation ⋮ Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations ⋮ Global regularity for a class of Monge-Ampère type equations ⋮ Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interior a priori estimates for solutions of fully nonlinear equations
• Two remarks on Monge-Ampère equations
• A localization theorem and boundary regularity for a class of degenerate Monge-Ampere equations
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• On a real Monge-Ampère functional
• Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• REGULARITY FOR MONGE-AMPERE EQUATION NEAR THE BOUNDARY
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation

This page was built for publication: Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions