{"title":"论沿边穿孔域中有漂移的泊松方程解的高积分性","authors":"G.A. Chechkin, T.P. Chechkina","doi":"10.1134/S1061920824030051","DOIUrl":null,"url":null,"abstract":"<p> In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). </p><p> <b> DOI</b> 10.1134/S1061920824030051 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"407 - 417"},"PeriodicalIF":1.7000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary\",\"authors\":\"G.A. Chechkin, T.P. Chechkina\",\"doi\":\"10.1134/S1061920824030051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). </p><p> <b> DOI</b> 10.1134/S1061920824030051 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"31 3\",\"pages\":\"407 - 417\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-10-03\",\"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/S1061920824030051\",\"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/S1061920824030051","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}
引用次数: 0
摘要
在本文中，我们考虑了在沿边界穿孔的域中存在漂移的线性二阶椭圆问题。在空腔边界上设置同质 Dirichlet 条件，在域外部边界上设置同质 Neumann 条件，我们证明了问题解梯度的高可整性（Boyarsky-Meyers 估计）。 doi 10.1134/s1061920824030051
On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary
In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate).
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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