Serena Guarino Lo Bianco, Domenico Angelo La Manna, B. Velichkov
{"title":"A two-phase problem with Robin conditions on the free boundary","authors":"Serena Guarino Lo Bianco, Domenico Angelo La Manna, B. Velichkov","doi":"10.5802/jep.139","DOIUrl":null,"url":null,"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.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/jep.139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
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.