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A two-phase problem with Robin conditions on the free boundary
[Un problème à frontière libre à deux phases avec conditions au bord de Robin]
Serena Guarino Lo Bianco1 ; Domenico Angelo La Manna2 ; Bozhidar Velichkov3
1 Università degli studi di Napoli “Federico II”, Dipartimento di Agraria Via Università 100, 80055 Portici (NA), Italia
2 University of Jyvaskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014, Finland
3 Dipartimento di Matematica, Università di Pisa Largo Bruno Pontecorvo, 5, 56127 Pisa, Italia
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1-25.

Nous étudions pour la première fois un problème à frontière libre à deux phases pour lequel la solution satisfait à une condition de Robin au bord. Nous considérons le cas où la solution est continue au bord et nous montrons un résultat d’existence et de régularité pour les minimiseurs du problème variationnel associé. Enfin, nous donnons dans l’appendice un exemple d’une classe de minimiseurs avec une symétrie de Steiner.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.139
Classification : 35R35, 49Q10
Keywords: Free boundary problems, two-phase, Robin boundary conditions, regularity
Mot clés : Problèmes à frontière libre, deux phases, conditions au bord de Robin, régularité
Serena Guarino Lo Bianco 1 ; Domenico Angelo La Manna 2 ; Bozhidar Velichkov 3

1 Università degli studi di Napoli “Federico II”, Dipartimento di Agraria Via Università 100, 80055 Portici (NA), Italia
2 University of Jyvaskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014, Finland
3 Dipartimento di Matematica, Università di Pisa Largo Bruno Pontecorvo, 5, 56127 Pisa, Italia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A two-phase problem with {Robin} conditions on the free boundary},
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Serena Guarino Lo Bianco; Domenico Angelo La Manna; Bozhidar Velichkov. A two-phase problem with Robin conditions on the free boundary. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1-25. doi : 10.5802/jep.139. https://jep.centre-mersenne.org/articles/10.5802/jep.139/

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