English

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

Analysis of PDEs 2025-04-18 v1

Abstract

We study the Dirichlet problem for Monge-Amp\`ere equation in bounded convex polytopes. We give sharp conditions for the existence of global C2C^2 and C2,αC^{2,\alpha} convex solutions provided that a global C2C^2, convex subsolution exists.

Keywords

Cite

@article{arxiv.2504.12987,
  title  = {Global regularity for the Dirichlet problem of Monge-Amp\`ere equation in convex polytopes},
  author = {Genggeng Huang and Weiming Shen},
  journal= {arXiv preprint arXiv:2504.12987},
  year   = {2025}
}