Symmetry results for some overdetermined obstacle problems
Analysis of PDEs
2023-06-22 v1
Abstract
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof avoids the method of moving planes; instead, it leverages the comparison principle and the fact that the solution of the obstacle problem is superharmonic within its domain. The second proof utilizes a suitable version of Serrin's method of moving planes.
Cite
@article{arxiv.2306.12124,
title = {Symmetry results for some overdetermined obstacle problems},
author = {Nicola De Nitti and Shigeru Sakaguchi},
journal= {arXiv preprint arXiv:2306.12124},
year = {2023}
}
Comments
10 pages, 2 figures