Complete classification of global solutions to the obstacle problem
Analysis of PDEs
2022-08-22 v2
Abstract
The characterization of global solutions to the obstacle problems in , 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.
Cite
@article{arxiv.2208.03108,
title = {Complete classification of global solutions to the obstacle problem},
author = {Simon Eberle and Alessio Figalli and Georg S. Weiss},
journal= {arXiv preprint arXiv:2208.03108},
year = {2022}
}