{"title":"外域的混合双调和Dirichlet-Neumann问题","authors":"H. Matevossian","doi":"10.17516/1997-1397-2020-13-6-755-762","DOIUrl":null,"url":null,"abstract":"We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"22 2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains\",\"authors\":\"H. Matevossian\",\"doi\":\"10.17516/1997-1397-2020-13-6-755-762\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem\",\"PeriodicalId\":422202,\"journal\":{\"name\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"volume\":\"22 2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2020-13-6-755-762\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University. Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2020-13-6-755-762","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains
We study the unique solvability of the mixed Dirichlet-Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem has a bounded Dirichlet integral with weight |x|a. Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of the problem or present exact formulas for the dimension of the space of solutions of the mixed Dirichlet-Neumann problem
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