{"title":"Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains","authors":"Teo Kukuljan","doi":"10.3934/dcds.2021207","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in <i>C</i><sup>1</sup> and <i>C</i><sup><i>k</i>, <i>α</i></sup> domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.</p><p style='text-indent:20px;'>As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.</p>","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Continuous Dynamical Systems - S","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2021207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in C1 and Ck, α domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.
As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.
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