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Characterizing compact coincidence sets in the obstacle problem -- a short proof
- Publication Year :
- 2020
-
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 $\{u=0 \}$ of a global solution $u$ is bounded with nonempty interior then it is an ellipsoid.
- Subjects :
- Mathematics - Analysis of PDEs
35R35, 35B65
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2005.10490
- Document Type :
- Working Paper