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arXiv · 1501.06498

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

Nicola Garofalo·Arshak Petrosyan·Mariana Smit Vega Garcia
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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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Nicola Garofalo, Arshak Petrosyan, Mariana Smit Vega Garcia. 2015-01-26. An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients. https://arxiv.org/abs/1501.06498

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