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.
A two-phase problem with Robin conditions on the free boundary / Lo Bianco, S. G.; la Manna, D. A.; Velichkov, B.. - In: JOURNAL DE L'ÉCOLE POLYTECHNIQUE. MATHÉMATIQUES. - ISSN 2429-7100. - 8:(2020), pp. 1-25. [10.5802/JEP.139]
A two-phase problem with Robin conditions on the free boundary
Lo Bianco S. G.;
2020
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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