Global C^1,α regularity for Monge-Ampère equations on planar convex domains

2025/01/28 by Qing Han, Jiakun Liu, Han, Qing +3
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2501.17337

openalex publication_date 2025/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation det D²u = f on strictly convex but not uniformly convex domain Ω.

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