V.Ya. Gutlyanskiĭ, V.I. Ryazanov, E.A. Sevost’yanov, E. Yakubov
{"title":"On the Dirichlet problem for A-harmonic functions","authors":"V.Ya. Gutlyanskiĭ, V.I. Ryazanov, E.A. Sevost’yanov, E. Yakubov","doi":"10.15407/dopovidi2023.04.011","DOIUrl":null,"url":null,"abstract":"We study the Dirichlet boundary value problem with continuous boundary data for the A-harmonic equations div[A grad u] = 0 in an arbitrary bounded domain D of the complex plane £ with no boundary component degenerated to a single point. We provide integral criteria, including the BMO and FMO criteria expressed in terms of A (z), for the existence of weak solutions to the problem. We also discuss the connections between A-harmonic functions and potential theory.","PeriodicalId":20898,"journal":{"name":"Reports of the National Academy of Sciences of Ukraine","volume":"64 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports of the National Academy of Sciences of Ukraine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15407/dopovidi2023.04.011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We study the Dirichlet boundary value problem with continuous boundary data for the A-harmonic equations div[A grad u] = 0 in an arbitrary bounded domain D of the complex plane £ with no boundary component degenerated to a single point. We provide integral criteria, including the BMO and FMO criteria expressed in terms of A (z), for the existence of weak solutions to the problem. We also discuss the connections between A-harmonic functions and potential theory.
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