{"title":"一般无界域中 $BMO$ 类型向量场的赫尔姆霍兹分解","authors":"Y. Giga, Zhongyang Gu","doi":"10.57262/ade029-0506-389","DOIUrl":null,"url":null,"abstract":"We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n \\geq 3$, we establish its Helmholtz decomposition for arbitrary uniformly $C^3$ domain in $\\mathbf{R}^n$.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains\",\"authors\":\"Y. Giga, Zhongyang Gu\",\"doi\":\"10.57262/ade029-0506-389\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n \\\\geq 3$, we establish its Helmholtz decomposition for arbitrary uniformly $C^3$ domain in $\\\\mathbf{R}^n$.\",\"PeriodicalId\":53312,\"journal\":{\"name\":\"Advances in Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/ade029-0506-389\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/ade029-0506-389","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains
We consider a space of $L^2$ vector fields with bounded mean oscillation whose ``normal'' component to the boundary is well-controlled. In the case when the dimension $n \geq 3$, we establish its Helmholtz decomposition for arbitrary uniformly $C^3$ domain in $\mathbf{R}^n$.
期刊介绍：
Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.
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