V. Gutlyanskiĭ, V. Ryazanov, E. Sevost’yanov, E. Yakubov
{"title":"关于微分Beltrami方程的Dirichlet问题","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":"{\"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}","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
摘要
本文研究了复平面上任意单连通有界域D上连续边界数据的Dirichlet问题,其中f满足退化的Beltrami方程a. e. in .中。我们用BMO和FMO判据以及其他一些积分判据给出了上述问题正则离散开解的存在性和表示。
On the Dirichlet problem for de ge nerate Beltrami equations
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.