An epiperimetric inequality for the lower dimensional obstacle problem

2017/09/04 by Geraci, Francesco
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.00996

Abstract

In this paper we give a proof of an epiperimetric inequality in the setting of the lower dimensional obstacle problem. The inequality was introduced by Weiss (Invent. Math., 138 (1999), no. 1, 23-50) for the classical obstacle problem and has striking consequences concerning the regularity of the free-boundary. Our proof follows the approach of Focardi and Spadaro (Adv. Differential Equations 21 (2015), no 1-2, 153-200.) which uses an homogeneity approach and a Γ-convergence analysis.

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