An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients

Abstract

In this paper we establish the C1,β regularity of the regular part of the free boundary in the Signorini problem for elliptic operators with variable Lipschitz coefficients. This work is a continuation of the recent paper [12], where two of us established the interior optimal regularity of the solution. Two of the central results of the present work are a new monotonicity formula and a new epiperimetric inequality.