English

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 {u=0}\{u=0 \} of a global solution uu is bounded with nonempty interior then it is an ellipsoid.

Keywords

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}
}
R2 v1 2026-06-23T15:42:31.133Z