{"title":"C1和Ck， α域上的高阶抛物边界Harnack不等式","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":"{\"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}","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}
Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains
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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