{"title":"具有奇异数据的某些椭圆问题解的 Marcinkiewicz 估计数","authors":"Lucio Boccardo, Luigi Orsina","doi":"10.1007/s11118-024-10140-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper we prove regularity result for solutions of the boundary value problem </p><span>$$ \\left\\{ \\begin{array}{cl} -{{\\,\\textrm{div}\\,}}(M(x)\\,\\nabla u) + u = -{{\\,\\textrm{div}\\,}}(u\\,E(x)) + f(x)\\,, &{} \\text{ in }\\,\\, \\Omega , \\\\ u = 0\\,, &{} \\text{ on }\\,\\,\\partial \\Omega , \\end{array} \\right. $$</span><p>with the vector field <i>E</i>(<i>x</i>) and the function <i>f</i>(<i>x</i>) belonging to some Marcinkiewicz spaces.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Marcinkiewicz Estimates for Solutions of Some Elliptic Problems with Singular Data\",\"authors\":\"Lucio Boccardo, Luigi Orsina\",\"doi\":\"10.1007/s11118-024-10140-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we prove regularity result for solutions of the boundary value problem </p><span>$$ \\\\left\\\\{ \\\\begin{array}{cl} -{{\\\\,\\\\textrm{div}\\\\,}}(M(x)\\\\,\\\\nabla u) + u = -{{\\\\,\\\\textrm{div}\\\\,}}(u\\\\,E(x)) + f(x)\\\\,, &{} \\\\text{ in }\\\\,\\\\, \\\\Omega , \\\\\\\\ u = 0\\\\,, &{} \\\\text{ on }\\\\,\\\\,\\\\partial \\\\Omega , \\\\end{array} \\\\right. $$</span><p>with the vector field <i>E</i>(<i>x</i>) and the function <i>f</i>(<i>x</i>) belonging to some Marcinkiewicz spaces.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11118-024-10140-w\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11118-024-10140-w","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文证明了边界值问题解的正则性结果 $$ \left\{ \begin{array}{cl} -{\textrm{div}\,}}(M(x)\,\nabla u) + u = -{\textrm{div}\,}}(u\,E(x))+ f(x)\,, &{}\u = 0\,, &{}\text{ on }\,\partial\Omega , \end{array}\是的$$with the vector field E(x) and the function f(x) belonging to some Marcinkiewicz spaces.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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