The two membranes problem for different operators
Analysis of PDEs
2016-01-12 v1
Abstract
We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the H\"older continuity of the solutions and we develop a viscosity solution approach to this problem. Then we obtain regularity of the solutions provided that the orders of the two operators are different. In the special case when one operator coincides with the fractional Laplacian, we obtain the optimal regularity and a characterization of the free boundary.
Keywords
Cite
@article{arxiv.1601.02548,
title = {The two membranes problem for different operators},
author = {L. Caffarelli and D. De Silva and O. Savin},
journal= {arXiv preprint arXiv:1601.02548},
year = {2016}
}