On a two-phase free boundary problem ruled by the infinity Laplacian
Analysis of PDEs
2020-06-09 v2
Abstract
In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in are universally Lipschitz continuous in , which is the optimal regularity for the problem. We make a new use of the Ishii-Lions' method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.
Cite
@article{arxiv.1812.04782,
title = {On a two-phase free boundary problem ruled by the infinity Laplacian},
author = {Damião J. Araújo and Eduardo Teixeira and José Miguel Urbano},
journal= {arXiv preprint arXiv:1812.04782},
year = {2020}
}
Comments
11 pages, 1 figure, LaTeX;