{"title":"关于外域中的Poisson方程","authors":"W. Varnhorn","doi":"10.33205/cma.1143800","DOIUrl":null,"url":null,"abstract":"We construct a solution of the Poisson equation in exterior domains $\\Omega \\subset \\mathbb R^n,\\;n \\ge 2,$ in homogeneous Lebesgue spaces $L^{2,q}(\\Omega),;1 < q <\\infty,$ with methods of potential theory and integral equations. We investigate the corresponding null spaces and prove that its dimensions is equal to $n+1$ independent of $q$.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the Poisson equation in exterior domains\",\"authors\":\"W. Varnhorn\",\"doi\":\"10.33205/cma.1143800\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct a solution of the Poisson equation in exterior domains $\\\\Omega \\\\subset \\\\mathbb R^n,\\\\;n \\\\ge 2,$ in homogeneous Lebesgue spaces $L^{2,q}(\\\\Omega),;1 < q <\\\\infty,$ with methods of potential theory and integral equations. We investigate the corresponding null spaces and prove that its dimensions is equal to $n+1$ independent of $q$.\",\"PeriodicalId\":36038,\"journal\":{\"name\":\"Constructive Mathematical Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33205/cma.1143800\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/cma.1143800","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We construct a solution of the Poisson equation in exterior domains $\Omega \subset \mathbb R^n,\;n \ge 2,$ in homogeneous Lebesgue spaces $L^{2,q}(\Omega),;1 < q <\infty,$ with methods of potential theory and integral equations. We investigate the corresponding null spaces and prove that its dimensions is equal to $n+1$ independent of $q$.
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