Characterizing compact coincidence sets in the obstacle problem -- a short proof

2020/05/21 by Simon Eberle, Eberle, Simon, Georg S. Weiss +1 · 1 citation
Computer Science · Mathematics · #35B65 #35R35 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Variational Analysis #math.AP #msc:35B65 #msc:35R35

paper · pdf · doi:10.48550/arxiv.2005.10490

openalex publication_date 2020/05/21 · arxiv created 2020/06/03 · arxiv updated 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

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• Global solutions to the thin obstacle problem with superquadratic growth

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