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arXiv · 2310.09034

The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Amp\`ere Equations

Ruosi Chen·Huaiyu Jian
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Abstract

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

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Ruosi Chen, Huaiyu Jian. 2023-10-13. The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Amp\`ere Equations. https://arxiv.org/abs/2310.09034

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