- Research Article
- Open Access
Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems
- Fausto Ferrari1, 2Email author and
- Sandro Salsa3
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.
Keywords
Authors’ Affiliations
References
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