Vol. 7, No. 2, 2014

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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
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 C1,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