Global regularity for the Dirichlet problem of Monge-Ampère equation in convex polytopes

2025/04/17 by Genggeng Huang, Weiming Shen, Huang, Genggeng +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.12987

openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Dirichlet problem for Monge-Ampère equation in bounded convex polytopes. We give sharp conditions for the existence of global C² and C^2,α convex solutions provided that a global C², convex subsolution exists.

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