Global \(C^{1,\alpha}\) regularity for Monge-Ampère equation and convex envelope

DOI10.1007/s00205-022-01757-5zbMath1496.35223OpenAlexW4214711542MaRDI QIDQ2123133

Lan Tang, Xu-Jia Wang, Luis A. Caffarelli

Publication date: 8 April 2022

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-022-01757-5

zbMATH Keywords

Dirichlet problemMonge-Ampère equationoptimal regularity

Mathematics Subject Classification ID

Boundary values of solutions to elliptic equations and elliptic systems (35J67) Monge-Ampère equations (35J96)

Related Items (1)

Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of the homogeneous Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• The Dirichlet problem for the degenerate Monge-Ampère equation
• The Dirichlet problem for the multidimensional Monge-Ampère equation
• The Dirichlet problem for the degenerate elliptic Monge-Ampère equation
• On the Dirichlet problem for degenerate Monge-Ampère equations.
• Boundary Hölder gradient estimates for the Monge-Ampère equation
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• Differentiability of convex envelopes
• The Dirichlet problem for the convex envelope
• A note on the degeneracy of convex solutions to monge amperé equation
• On the Smoothness of Convex Envelopes
• On second derivative estimates for equations of Monge-Ampère type
• BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS
• The convex envelope is the solution of a nonlinear obstacle problem
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Some regularity properties of solutions of Monge Ampère equation
• Some Counterexamples to the Regularity of Monge-Ampere Equations
• REGULARITY FOR MONGE-AMPERE EQUATION NEAR THE BOUNDARY
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
• Optimal regularity of the convex envelope

This page was built for publication: Global \(C^{1,\alpha}\) regularity for Monge-Ampère equation and convex envelope