Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions

DOI10.3934/cpaa.2020267zbMath1460.35184OpenAlexW3103276248MaRDI QIDQ2658842

Mengni Li

Publication date: 24 March 2021

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2020267

zbMATH Keywords

Dirichlet problemconvex domainboundary regularityMonge-Ampère-type equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Monge-Ampère equations (35J96)

Cites Work

• Multiple solutions of the \(L_{p}\)-Minkowski problem
• Bernstein theorem and regularity for a class of Monge-Ampère equations
• The Monge-Ampère equation and its applications
• Schauder estimates for degenerate Monge-Ampère equations and smoothness of the eigenfunctions
• Global Hölder estimates for equations of Monge-Ampère type
• On the Dirichlet problem for degenerate Monge-Ampère equations.
• Elliptic partial differential equations of second order
• Optimal boundary regularity for a singular Monge-Ampère equation
• Boundary \(C^{2, \alpha}\) estimates for Monge-Ampère type equations
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• Global smoothness for a singular Monge-Ampère equation
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The Dirichlet problem for the equation of prescribed Gauss curvature
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
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