On boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations

Nam Q. Le; Ovidiu Savin

On boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations

Analysis of PDEs 2013-08-27 v2

Authors: Nam Q. Le , Ovidiu Savin

Abstract

In this paper, we establish boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations with $L^{p}$ ( $n<p\leq\infty$ ) right hand side and $C^{1,\gamma}$ boundary values under natural assumptions on the domain, boundary data and the Monge-Amp\`ere measure. These estimates extend our previous boundary regularity results for solutions to the linearized Monge-Amp\`ere equations with bounded right hand side and $C^{1, 1}$ boundary data.

Keywords

monge-ampère equation linearized equation boundary regularity hölder gradient estimates elliptic pde

Cite

@article{arxiv.1303.3305,
  title  = {On boundary H\"older gradient estimates for solutions to the linearized Monge-Amp\`ere equations},
  author = {Nam Q. Le and Ovidiu Savin},
  journal= {arXiv preprint arXiv:1303.3305},
  year   = {2013}
}

Comments

to appear in Proc. Amer. Math. Soc

Related papers

View all related →