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  • Research Article
  • Open Access

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

  • Received: 29 May 2006
  • Accepted: 10 September 2006
  • Published:

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

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

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Authors’ 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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