Partial Regularity for Singular Solutions to the Monge‐Ampère Equation

DOI10.1002/cpa.21534zbMath1317.35079arXiv1304.2706OpenAlexW2963508558MaRDI QIDQ5252286

Connor Mooney

Publication date: 29 May 2015

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

Full work available at URL: https://arxiv.org/abs/1304.2706

zbMATH Keywords

partial regularityHausdorff measure.Monge-Ampère inequality

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60)

Related Items (15)

Dimension of the minimum set for the real and complex Monge-Ampère equations in critical Sobolev spaces ⋮ The Monge–Ampère equation and its link to optimal transportation ⋮ Singular Solutions to Monge-Ampère Equation ⋮ Strict convexity and \(C^{1,\alpha}\) regularity of potential functions in optimal transportation under condition A3w ⋮ THE GROWTH OF SOLUTIONS OF MONGE–AMPÈRE EQUATIONS IN HALF SPACES AND ITS APPLICATION ⋮ Metric SYZ conjecture and non-Archimedean geometry ⋮ Singular structures in solutions to the Monge-Ampère equation with point masses ⋮ Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces ⋮ A comparison of the real and non-Archimedean Monge-Ampère operator ⋮ Quantitative stochastic homogenization of elliptic equations in nondivergence form ⋮ Solutions to the Monge-Ampère equation with polyhedral and Y-shaped singularities ⋮ Asymptotic behavior at infinity of solutions of Monge-Ampère equations in half spaces ⋮ The minimum sets and free boundaries of strictly plurisubharmonic functions ⋮ Quantitative logarithmic Sobolev inequalities and stability estimates ⋮ Quantitative homogenization in a balanced random environment

Cites Work

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• On the structure of singular sets of convex functions
• On the singularities of convex functions
• \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
• Unique continuation for fully nonlinear elliptic equations
• A note on the degeneracy of convex solutions to monge amperé equation
• Unique continuation for elliptic operators: A geometric-variational approach
• The Monge-Ampère equation

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