Regularity of subelliptic Monge-Ampère equations in the plane

DOI10.1090/S0002-9947-09-04640-6zbMath1173.35470MaRDI QIDQ3394968

Pengfei Guan, Eric T. Sawyer

Publication date: 11 September 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

regularityMonge-Ampère equationsmooth compact oriented surface

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05)

Related Items (10)

Isometric embedding with nonnegative Gauss curvature under the graph setting ⋮ Gevrey regularity of subelliptic Monge-Ampère equations in the plane ⋮ Global bifurcation and convex solutions for the Monge-Ampère equation ⋮ Two Whyburn type topological theorems and its applications to Monge-Ampère equations ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ On Monge-Ampère equations with homogenous right-hand sides ⋮ Unilateral Global Bifurcation for Eigenvalue Problems with Homogeneous Operator ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ The Weyl problem of isometric immersions revisited ⋮ Regularity of the homogeneous Monge-Ampère equation

Cites Work

• A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
• \(C^ 2\) a priori estimates for degenerate Monge-Ampère equations
• Isometric embeddings of surfaces with nonnegative curvature in \(\mathbb{R}^ 3\)
• The Weyl problem with nonnegative Gauss curvature
• Regularity of a class of quasilinear degenerate elliptic equations
• On the Dirichlet problem for degenerate Monge-Ampère equations.
• Isometric embedding of the 2-sphere with non negative curvature in \(\mathbb{R}^ 3\)
• Regularity of subelliptic Monge-Ampère equations
• On Monge-Ampère equations with homogenous right-hand sides
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The Weyl and Minkowski problems in differential geometry in the large

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