Calculus of Variations and Geometric Measure Theory

S. Eberle - A. Figalli - G. S. Weiss

Complete classification of global solutions to the obstacle problem

created by figalli on 10 Oct 2024

[BibTeX]

Accepted Paper

Inserted: 10 oct 2024
Last Updated: 10 oct 2024

Journal: Ann. of Math.
Year: 2024

Abstract:

The characterization of global solutions to the obstacle problems in $\mathbb{R}^N$, or equivalently of null quadrature domains, has been studied for 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 halfspace, an ellipsoid, a paraboloid, or a cylinder with an ellipsoid or a paraboloid as base.


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