{"title":"A connection between regularity and Dirichlet problems for non-divergence elliptic equations","authors":"J. Rivera-Noriega","doi":"10.7153/DEA-2018-10-05","DOIUrl":null,"url":null,"abstract":"We observe that a version of Poincaré’s inequality for positive solutions to second order linear non-divergence form equations vanishing on a portion of the boundary, implies a natural connection between Lp Dirichlet and Lq Regularity problems for this type of equations.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"64 1","pages":"75-86"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-2018-10-05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We observe that a version of Poincaré’s inequality for positive solutions to second order linear non-divergence form equations vanishing on a portion of the boundary, implies a natural connection between Lp Dirichlet and Lq Regularity problems for this type of equations.
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