[Un problème à frontière libre à deux phases avec conditions au bord de Robin]
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.
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DOI : 10.5802/jep.139
Keywords: Free boundary problems, two-phase, Robin boundary conditions, regularity
Mots-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
CC-BY 4.0
@article{JEP_2021__8__1_0,
author = {Serena Guarino Lo Bianco and Domenico Angelo La Manna and Bozhidar Velichkov},
title = {A two-phase problem with {Robin} conditions on the free boundary},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1--25},
publisher = {\'Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.139},
mrnumber = {4180258},
zbl = {07282220},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.139/}
}
TY - JOUR AU - Serena Guarino Lo Bianco AU - Domenico Angelo La Manna AU - Bozhidar Velichkov TI - A two-phase problem with Robin conditions on the free boundary JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1 EP - 25 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.139/ DO - 10.5802/jep.139 LA - en ID - JEP_2021__8__1_0 ER -
%0 Journal Article %A Serena Guarino Lo Bianco %A Domenico Angelo La Manna %A Bozhidar Velichkov %T A two-phase problem with Robin conditions on the free boundary %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 1-25 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.139/ %R 10.5802/jep.139 %G en %F JEP_2021__8__1_0
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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