English

Global $C^{1,\alpha}$ regularity for Monge-Amp\`ere equations on planar convex domains

Analysis of PDEs 2025-01-30 v1

Abstract

In this paper, we establish the global H\"older gradient estimate for solutions to the Dirichlet problem of the Monge-Amp\`ere equation detD2u=f\det D^2u = f on strictly convex but not uniformly convex domain Ω\Omega.

Keywords

Cite

@article{arxiv.2501.17337,
  title  = {Global $C^{1,\alpha}$ regularity for Monge-Amp\`ere equations on planar convex domains},
  author = {Qing Han and Jiakun Liu and Yang Zhou},
  journal= {arXiv preprint arXiv:2501.17337},
  year   = {2025}
}