Two-phase problems with distributed sources: regularity of the free boundary

De Silva, Daniela; Ferrari, Fausto; Salsa, Sandro

doi:10.2140/apde.2014.7.267

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Two-phase problems with distributed sources: regularity of the free boundary

Daniela De Silva, Fausto Ferrari and Sandro Salsa

Vol. 7 (2014), No. 2, 267–310

DOI: 10.2140/apde.2014.7.267

Abstract

We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with nonzero right-hand side. We prove that Lipschitz or flat free boundaries are $C^{1, γ}$ . In particular, viscosity solutions are indeed classical.

Keywords

two-phase free boundary problems, regularity

Mathematical Subject Classification 2010

Primary: 35B65

Milestones

Received: 31 October 2012

Accepted: 2 January 2014

Published: 30 May 2014

Authors

Daniela De Silva
Department of Mathematics Barnard College, Columbia University New York, NY 10027 United States

Fausto Ferrari
Dipartimento di Matematica Università di Bologna Piazza di Porta S. Donato, 5 I-40126 Bologna Italy

Sandro Salsa
Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci, 32 I-20133 Milano Italy

Vol. 7, No. 2, 2014