A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations

DOI10.1016/j.aim.2004.05.009zbMath1072.35052OpenAlexW1968362061MaRDI QIDQ555893

Richard L. Wheeden, Eric T. Sawyer, Cristian Rios

Publication date: 10 June 2005

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2004.05.009

zbMATH Keywords

Monge-Ampèreequation of prescribed Gaussian curvaturepartial Legendre, regularitytheory of De Giorgi-Nash-Moser

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate elliptic equations (35J70) A priori estimates in context of PDEs (35B45) Subelliptic equations (35H20)

Related Items (11)

Evans-Krylov estimates for a nonconvex Monge-Ampère equation ⋮ Hypoellipticity for infinitely degenerate quasilinear equations and the Dirichlet problem ⋮ Gevrey regularity of subelliptic Monge-Ampère equations in the plane ⋮ Degenerate Sobolev spaces and regularity of subelliptic equations ⋮ Regularity of subelliptic Monge-Ampère equations ⋮ Regularity of degenerate Monge-Ampère and prescribed Gaussian curvature equations in two dimensions ⋮ Regularity of subelliptic Monge-Ampère equations in the plane ⋮ Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients ⋮ Existence of Global Smooth Solutions to Dirichlet Problem for Degenerate Elliptic Monge–Ampere Equations ⋮ Partial Legendre transforms of non-linear equations ⋮ Regularity of the homogeneous Monge-Ampère equation

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