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Complete classification of global solutions to the obstacle problem
- Publication Year :
- 2022
-
Abstract
- The characterization of global solutions to the obstacle problems in $\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by proving the following long-standing conjecture: The coincidence set of a global solution to the obstacle problem is either a half-space, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.
- Subjects :
- Mathematics - Analysis of PDEs
35R35, 35B65
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.03108
- Document Type :
- Working Paper