A two-phase problem with Robin conditions on the free boundary
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.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Les Éditions de l'École polytechnique
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202108184541Use this for linking
Review status
Peer reviewed
ISSN
2429-7100
DOI
https://doi.org/10.5802/jep.139
Language
English
Published in
Journal de l'École polytechnique : Mathématiques
Citation
- Guarino Lo Bianco, S., La Manna, D. A., & Velichkov, B. (2021). A two-phase problem with Robin conditions on the free boundary. Journal de l'École polytechnique : Mathématiques, 8, 1-25. https://doi.org/10.5802/jep.139
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Funder(s)
Research Council of Finland
Funding program(s)
Research costs of Academy Research Fellow, AoF
Akatemiatutkijan tutkimuskulut, SA
Additional information about funding
The first author was partially supported by PRIN 2017 Nonlinear Differential Problems via Vari ational, Topological and Set-valued Methods (Grant 2017AYM8XW) and the INdAM-GNAMPA project 2020 “Problemi di ottimizzazione con vincoli via trasporto ottimo e incertezza”. The second author was partially supported by the Academy of Finland grant 314227. The third author has been partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement VAREG, No. 853404)
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