Characterizing compact coincidence sets in the obstacle problem -- a short proof
Analysis of PDEs
2020-06-04 v2
Abstract
Motivated by the almost completely open problem of characterizing unbounded coincidence sets of global solutions of the classical obstacle problem in higher dimensions, we give in this note a concise and easy-to-extend proof of the known fact that if the coincidence set of a global solution is bounded with nonempty interior then it is an ellipsoid.
Cite
@article{arxiv.2005.10490,
title = {Characterizing compact coincidence sets in the obstacle problem -- a short proof},
author = {Simon Eberle and Georg S. Weiss},
journal= {arXiv preprint arXiv:2005.10490},
year = {2020}
}