An epiperimetric inequality for the lower dimensional obstacle problem

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) 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. Differ. Equ.21(2015) 153–200] which uses an homogeneity approach and aΓ-convergence analysis.