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

2015/01/26 by Garofalo, Nicola, Petrosyan, Arshak, Garcia, Mariana Smit Vega
#35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.06498

Abstract

In this paper we establish the C^1,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 [GSVG14], 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.

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• An epiperimetric inequality approach to the parabolic Signorini problem
• Optimal regularity for the Signorini problem
• Optimal regularity for the variable coefficients parabolic Signorini problem
• Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
• Higher regularity of the free boundary in the elliptic Signorini problem