{"title":"Lᵖ Regularity of the Solution of the Heat Equation with Discontinuous Coefficients","authors":"Selma Kouicem, W. Chikouche","doi":"10.17516/1997-1397-2020-13-466-479","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the transmission problem for the heat equation on a bounded plane sector in Lᵖ-Sobolev spaces. By Applying the theory of the sums of operators of Da Prato-Grisvard and Dore-Venni, we prove that the solution can be splited into a regular part in Lp-Sobolev space and an explicit singular part","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University. Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2020-13-466-479","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we consider the transmission problem for the heat equation on a bounded plane sector in Lᵖ-Sobolev spaces. By Applying the theory of the sums of operators of Da Prato-Grisvard and Dore-Venni, we prove that the solution can be splited into a regular part in Lp-Sobolev space and an explicit singular part
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