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arXiv · 2504.12987

Global regularity for the Dirichlet problem of Monge-Amp\`ere equation in convex polytopes

Genggeng Huang·Weiming Shen
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Abstract

We study the Dirichlet problem for Monge-Amp\`ere equation in bounded convex polytopes. We give sharp conditions for the existence of global $C^2$ and $C^{2,\alpha}$ convex solutions provided that a global $C^2$, convex subsolution exists.

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Genggeng Huang, Weiming Shen. 2025-04-17. Global regularity for the Dirichlet problem of Monge-Amp\`ere equation in convex polytopes. https://arxiv.org/abs/2504.12987

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