Global regularity for the Dirichlet problem of Monge-Ampère equation in convex polytopes
Published: Apr 17, 2025
Last Updated: Apr 17, 2025
Authors:Genggeng Huang, Weiming Shen
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.