The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Ampère Equations

2023/10/13 by Chen, Ruosi, Jian, Huaiyu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.09034

Abstract

We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge-Ampère Equations: one is singular which is from the proper affine hyperspheres with constant mean curvature; the other is degenerate which is from the Monge-Ampère eigenvalue problem. As a result, we obtain the sharp boundary boundary estimates and the optimal global Hölder regularity for the two equations.

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