Global regularity for the Monge-Ampère equation with natural boundary condition

DOI10.4007/annals.2021.194.3.4zbMath1487.35214arXiv1802.07518OpenAlexW3213053170MaRDI QIDQ2058611

Jiakun Liu, Xu-Jia Wang, Shibing Chen

Publication date: 9 December 2021

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.07518

zbMATH Keywords

Monge-Ampère equationglobal regularity

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)

Related Items (7)

On the regularity of optimal transports between degenerate densities ⋮ Sharp boundary \(\varepsilon\)-regularity of optimal transport maps ⋮ Regularity of optimal mapping between hypercubes ⋮ Trivariate spline collocation methods for numerical solution to 3D Monge-Ampère equation ⋮ C2,α$C^{2,\alpha }$ regularity of free boundaries in optimal transportation ⋮ Global \(W^{2,1+\varepsilon}\) estimates for Monge-Ampère equation with natural boundary condition ⋮ Global regularity of optimal mappings in non-convex domains

Cites Work

• Unnamed Item
• Unnamed Item
• The Monge-Ampère equation and its applications
• Partial \(W^{2,p}\) regularity for optimal transport maps
• Boundary regularity of maps with convex potentials. II
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• Minimal Lagrangian diffeomorphisms between domains in the hyperbolic plane
• Free boundaries in optimal transport and Monge-Ampère obstacle problems
• A boundary value problem for minimal Lagrangian graphs
• Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Global regularity of optimal mappings in non-convex domains
• Regularity of optimal transport between planar convex domains
• Regularity of potential functions of the optimal transportation problem
• Boundary regularity for the Monge-Ampère and affine maximal surface equations
• On the (in)stability of the identity map in optimal transportation
• Convolutional wasserstein distances
• Global 𝑊^{2,𝑝} estimates for the Monge-Ampère equation
• The Monge–Ampère equation and its link to optimal transportation
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The neumann problem for equations of monge-ampère type
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Regularity of Mappings with a Convex Potential
• Boundary regularity of maps with convex potentials
• Elliptic Partial Differential Equations of Second Order
• On the second boundary value problem for equations of Monge-Ampère type.
• Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
• Continuity Estimates for the Monge–Ampère Equation
• Optimal Transport
• The Monge-Ampère equation

This page was built for publication: Global regularity for the Monge-Ampère equation with natural boundary condition