Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

On two phase free boundary problems governed by elliptic equations with distributed sources

Pages: 673 - 693, Volume 7, Issue 4, August 2014      doi:10.3934/dcdss.2014.7.673

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Daniela De Silva - Department of Mathematics, Barnard College, Columbia University, 2990 Broadway, New York, NY 10027, United States (email)
Fausto Ferrari - Dipartimento di Matematica dell'Università di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy (email)
Sandro Salsa - Dipartimento di Matematica del Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy (email)

Abstract: We present some recent progress on the analysis of two-phase free boundary problems governed by elliptic operators, with non-zero right hand side. We also discuss on several open questions, object of future investigations.

Keywords:  Two-phase problems, free boundary problems, fully nonlinear operators, nonhomogeneous elliptic equations.
Mathematics Subject Classification:  Primary: 35J25, 35R35; Secondary: 35J60.

Received: November 2013;      Available Online: February 2014.