English

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 B1B_1 are universally Lipschitz continuous in B1/2B_{1/2}, 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.

Keywords

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;

R2 v1 2026-06-23T06:39:46.954Z