Existence, uniqueness and interior regularity of viscosity solutions for a class of Monge-Ampère type equations

DOI10.1016/j.jde.2024.09.024MaRDI QIDQ6644204

Mengni Li, You Li

Publication date: 27 November 2024

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemexistenceuniquenessinterior 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) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Monge-Ampère equations (35J96)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mirror symmetric solutions to the centro-affine Minkowski problem
• The Monge-Ampère equation and its applications
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Perron's method for Hamilton-Jacobi equations
• Global Hölder estimates for equations of Monge-Ampère type
• On the \(L_{p}\) Monge-Ampère equation
• Global regularity for a class of Monge-Ampère type equations
• On the Dirichlet problem for Monge-Ampère type equations
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• On a real Monge-Ampère functional
• Existence of entire solutions to the Monge-Ampère equation
• The Dirichlet problem for the equation of prescribed Gauss curvature
• 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
• On the existence of solutions of a class of Monge-Ampére equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• The dirichlet problem for a class of fully nonlinear elliptic equations
• The eigenvalue problem for the Monge-Ampère operator on general bounded convex domains
• The Monge-Ampère equation
• Sharp boundary regularity for some degenerate-singular Monge-Ampère equations on \(k\)-convex domain

This page was built for publication: Existence, uniqueness and interior regularity of viscosity solutions for a class of Monge-Ampère type equations