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

Boundary Value Problems volume 2007, Article number: 057049 (2006) Cite this article

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.

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Authors and Affiliations

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

    Fausto Ferrari

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

    Fausto Ferrari

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

    Sandro Salsa

Authors
  1. Fausto Ferrari
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  2. Sandro Salsa
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Correspondence to Fausto Ferrari.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ferrari, F., Salsa, S. Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems. Bound Value Probl 2007, 057049 (2006). https://doi.org/10.1155/2007/57049

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  • DOI: https://doi.org/10.1155/2007/57049

Keywords

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