Recent progresses on elliptic two-phase free boundary problems

Daniela De Silva; Fausto Ferrari; Sandro Salsa

doi:10.3934/dcds.2019239

Article Contents

2019, Volume 39, Issue 12: 6961-6978. Doi: 10.3934/dcds.2019239

This issue Previous Article On global solutions to semilinear elliptic equations related to the one-phase free boundary problem Next Article The method of energy channels for nonlinear wave equations

Recent progresses on elliptic two-phase free boundary problems

1.
Department of Mathematics, Barnard College, Columbia University, New York, NY 10027, USA
2.
Dipartimento di Matematica dell'Università di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy
3.
Dipartimento di Matematica del Politecnico di Milano, Leonardo da Vinci, 32, 20133 Milano, Italy

^* Corresponding author: Sandro Salsa
^* Corresponding author: Sandro Salsa

Received: September 30, 2018

Revised: October 31, 2018

Published: September 2019

D. D. is partially supported by the Tow Award. F. F. is partially supported by: INDAM-GNAMPA 2017-Regolarità delle soluzioni viscose per equazioni a derivate parziali non lineari degeneri, INDAM-GNAMPA 2018-Costanti critiche e problemi asintotici per equazioni completamente non lineari.

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We provide an overview of some recent results about the regularity of the solution and the free boundary for so-called two-phase free boundary problems driven by uniformly elliptic equations.

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Mathematics Subject Classification: Primary: 35R35, 35B65, 35J66.

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References

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