On Monge-Ampère equations with homogenous right-hand sides

DOI10.1002/cpa.20263zbMath1171.35341arXiv0706.3748OpenAlexW1946709974MaRDI QIDQ3625732

Ovidiu V. Savin, Panagiota Daskalopoulos

Publication date: 6 May 2009

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

Full work available at URL: https://arxiv.org/abs/0706.3748

zbMATH Keywords

radial behavior near the origintwo-dimensional degenerate Monge-Ampère equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Analyticity in context of PDEs (35A20)

Related Items (14)

Solvability of a class of singular fourth order equations of Monge-Ampère type ⋮ On the Preservation of Eccentricities of Monge–Ampère Sections ⋮ Interior estimates for the Monge-Ampère type fourth order equations ⋮ Isometric embedding with nonnegative Gauss curvature under the graph setting ⋮ Partial differential equations. Abstracts from the workshop held July 25--31, 2021 (hybrid meeting) ⋮ Global bifurcation and convex solutions for the Monge-Ampère equation ⋮ Addendum: 2D homogeneous solutions to the Euler equation ⋮ The Monge-Ampère equation with Guillemin boundary conditions ⋮ On the Dirichlet problem for a class of singular complex Monge-Ampère equations ⋮ A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations ⋮ Regularity of subelliptic Monge-Ampère equations in the plane ⋮ Interior $C^2$ estimate for Monge-Ampère equation in dimension two ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ The Weyl problem of isometric immersions revisited

Cites Work

• The Weyl problem with nonnegative Gauss curvature
• Regularity of a class of quasilinear degenerate elliptic equations
• Elliptic partial differential equations of second order
• Regularity of subelliptic Monge-Ampère equations in the plane
• Polar factorization and monotone rearrangement of vector‐valued functions
• Some regularity properties of solutions of Monge Ampère equation
• Boundary regularity of maps with convex potentials
• On the Existence of a Closed Convex Surface Realizing a Given Riemannian Metric
• The Weyl and Minkowski problems in differential geometry in the large
• The Monge-Ampère equation

This page was built for publication: On Monge-Ampère equations with homogenous right-hand sides