V. Gutlyanskiĭ, V. Ryazanov, E. Sevost’yanov, E. Yakubov
{"title":"On the Dirichlet problem for de ge nerate Beltrami equations","authors":"V. Gutlyanskiĭ, V. Ryazanov, E. Sevost’yanov, E. Yakubov","doi":"10.15407/dopovidi2023.03.009","DOIUrl":null,"url":null,"abstract":"We study the Dirichlet problem as with continuous boundary data in arbitrary simply connected bounded domains D of the complex plane where f satisfies the degenerate Beltrami equation a. e. in D. We give in terms of the BMO and FMO criteria as well as a number of other integral criteria on the existence and representation of regular discrete open solutions to the stated above problem.","PeriodicalId":20898,"journal":{"name":"Reports of the National Academy of Sciences of Ukraine","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-11","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/dopovidi2023.03.009","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 problem as with continuous boundary data in arbitrary simply connected bounded domains D of the complex plane where f satisfies the degenerate Beltrami equation a. e. in D. We give in terms of the BMO and FMO criteria as well as a number of other integral criteria on the existence and representation of regular discrete open solutions to the stated above problem.