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This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Research Article

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

Fausto Ferrari12* and Sandro Salsa3

Author Affiliations

1 Dipartimento di Matematica, Università di Bologna, Piazza di Porta S.~Donato 5, Bologna 40126, Italy

2 C.I.R.A.M., Via Saragozza 8, Bologna 40123, Italy

3 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 7, Milano 20133, Italy

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Boundary Value Problems 2007, 2007:057049  doi:10.1155/2007/57049


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/057049


Received:29 May 2006
Accepted:10 September 2006
Published:5 December 2006

© 2007 Ferrari and Salsa

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.

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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