A two-phase problem with Robin conditions on the free boundary

Published 31 Mar 2020 in math.AP | (2003.14139v2)

Abstract: We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers.

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