{"title":"论无界域多谐方程的纳维问题解法","authors":"H.A. Matevossian","doi":"10.1134/S1061920823040209","DOIUrl":null,"url":null,"abstract":"<p> The polyharmonic Navier problem is considered, the uniqueness (non-uniqueness) of its solution is studied in unbounded domains under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight <span>\\(|x|^a\\)</span>. Depending on the values of the parameter <span>\\(a\\)</span>, uniqueness theorems are proved and exact formulas are found for calculating the dimension of the space of solutions of the Navier problem for a polyharmonic equation in the exterior of a compact set and in a half-space. </p><p> <b> DOI</b> 10.1134/S1061920823040209 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"713 - 716"},"PeriodicalIF":1.7000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Solutions of the Navier Problem for a Polyharmonic Equation in Unbounded Domains\",\"authors\":\"H.A. Matevossian\",\"doi\":\"10.1134/S1061920823040209\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The polyharmonic Navier problem is considered, the uniqueness (non-uniqueness) of its solution is studied in unbounded domains under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight <span>\\\\(|x|^a\\\\)</span>. Depending on the values of the parameter <span>\\\\(a\\\\)</span>, uniqueness theorems are proved and exact formulas are found for calculating the dimension of the space of solutions of the Navier problem for a polyharmonic equation in the exterior of a compact set and in a half-space. </p><p> <b> DOI</b> 10.1134/S1061920823040209 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 4\",\"pages\":\"713 - 716\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823040209\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823040209","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
On Solutions of the Navier Problem for a Polyharmonic Equation in Unbounded Domains
The polyharmonic Navier problem is considered, the uniqueness (non-uniqueness) of its solution is studied in unbounded domains under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight \(|x|^a\). Depending on the values of the parameter \(a\), uniqueness theorems are proved and exact formulas are found for calculating the dimension of the space of solutions of the Navier problem for a polyharmonic equation in the exterior of a compact set and in a half-space.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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