# An epiperimetric inequality for the lower dimensional obstacle problem

created by geraci on 04 Sep 2017

[BibTeX]

Preprint

Inserted: 4 sep 2017
Last Updated: 4 sep 2017

Year: 2017

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 $\Gamma$-convergence analysis.