Boundary Value Problems

, 2007:057049 | Cite as

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

Open Access
Research Article
Part of the following topical collections:
  1. Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations

Abstract

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

Keywords

Differential Equation Partial Differential Equation Ordinary Differential Equation Weak Solution Functional Equation 

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Copyright information

© 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.

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.C.I.R.A.M.BolognaItaly
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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