%0 Journal Article
%T Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems
%A Fausto Ferrari
%A Sandro Salsa
%J Boundary Value Problems
%D 2006
%I Springer
%R 10.1155/2007/57049
%X Let L be a divergence form operator with Lipschitz continuous coefficients in a domain     , and let u be a continuous weak solution of Lu=0 in {u бщ бы  0}. In this paper, we show that if      satisfies a suitable differential inequality, then v    (x)=supB    (x)(x)u is a subsolution of Lu=0 away from its zero set. We apply this result to prove C1,   3 regularity of Lipschitz free boundaries in two-phase problems.
%U http://dx.doi.org/10.1155/2007/57049