New monotonicity formulas and the optimal regularity in the Signorini problem with variable coefficients

被引：28

作者：

Garofalo, Nicola ^{[1
]}

Garcia, Mariana Smit Vega ^{[2
]}

机构：

[1] Univ Padua, Dipartimento Ingn Civile & Ambientale DICEA, I-35131 Padua, Italy

[2] Univ Dusseldorf, Dept Math, D-40225 Dusseldorf, Germany

来源：

ADVANCES IN MATHEMATICS | 2014年 / 262卷

关键词：

Thin obstacle problem; Signorini problem; Optimal regularity; Free boundary problems; OBSTACLE PROBLEM; ELLIPTIC-OPERATORS; FREE-BOUNDARY; UNIQUE CONTINUATION;

D O I：

10.1016/j.aim.2014.05.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the interior Signorini, or lower-dimensional obstacl problem for a uniformly elliptic divergence form operator L = div(A(x)del) with Lipschitz continuous coefficients. Our main result states that, similarly to what happens when L = Delta, the variational solution has the optimal interior regularity C-loc(1,1/2) (Omega(+/-) U M), when M is a codimension one fiat manifold which supports the obstacle. We achieve this by proving some new monotonicity formulas for an appropriate generalizatio of the celebrated Almgren's frequency functional. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：682 / 750

页数：69

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