#### 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 ${C}^{1,\gamma }$. In particular, viscosity solutions are indeed classical.

##### Keywords
two-phase free boundary problems, regularity
Primary: 35B65
##### Milestones
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