Boundary Value Problems

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Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems

Boundary Value Problems20062007:057049

https://doi.org/10.1155/2007/57049

©  Ferrari and Salsa 2007

Received: 29 May 2006

Accepted: 10 September 2006

Published: 5 December 2006

Abstract

Let be a divergence form operator with Lipschitz continuous coefficients in a domain , and let be a continuous weak solution of in . In this paper, we show that if satisfies a suitable differential inequality, then is a subsolution of away from its zero set. We apply this result to prove regularity of Lipschitz free boundaries in two-phase problems.

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Authors’ Affiliations

(1)
Dipartimento di Matematica, Università di Bologna
(2)
C.I.R.A.M.
(3)
Dipartimento di Matematica, Politecnico di Milano

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© Ferrari and Salsa 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.