{"title":"Free boundary regularity in the fully nonlinear parabolic thin obstacle problem","authors":"Xi Hu, Lin Tang","doi":"10.1515/acv-2023-0126","DOIUrl":null,"url":null,"abstract":"\n <jats:p>We study the regularity of the free boundary in the fully nonlinear parabolic thin obstacle problem.\nUnder the assumption of time semiconvexity, our main result establishes that the free boundary is a <jats:inline-formula id=\"j_acv-2023-0126_ineq_9999\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:msup>\n <m:mi>C</m:mi>\n <m:mn>1</m:mn>\n </m:msup>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_acv-2023-0126_eq_0100.png\" />\n <jats:tex-math>C^{1}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> graph in <jats:italic>x</jats:italic> near any regular free boundary point.</jats:p>","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2023-0126","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the regularity of the free boundary in the fully nonlinear parabolic thin obstacle problem.
Under the assumption of time semiconvexity, our main result establishes that the free boundary is a C1C^{1} graph in x near any regular free boundary point.
期刊介绍：
Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.
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