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Compact contact sets of sub-quadratic solutions to the thin obstacle problem
- Publication Year :
- 2023
-
Abstract
- We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact contact set, we show that it must be an ellipsoid.<br />Comment: A uniqueness result is added to Theorem 1.1, thanks to the suggestion of one referee. Funding information is added
- Subjects :
- Mathematics - Analysis of PDEs
35R35, 35B65
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.03939
- Document Type :
- Working Paper