Sharp boundary regularity for some degenerate-singular Monge-Amp\`ere Equations on k-convex domain
Analysis of PDEs
2023-03-20 v1
Abstract
We introduce the concept of k-strictly convexity to describe the accurate convexity of convex domains some directions of which boundary may be flat. Basing this accurate convexity, we construct sub-solutions the Dirichlet problem for some degenerate-singular Monge-Amp\`ere type equations and prove the sharp boundary estimates for convex viscosity solutions of the problem. As a result, we obtain the optimal global H\"older regularity of the convex viscosity solutions.
Keywords
Cite
@article{arxiv.2303.09890,
title = {Sharp boundary regularity for some degenerate-singular Monge-Amp\`ere Equations on k-convex domain},
author = {Huaiyu Jian and Xianduo Wang},
journal= {arXiv preprint arXiv:2303.09890},
year = {2023}
}