{"title":"有不规则障碍物的奇异椭圆测量数据问题","authors":"Sun-Sig Byun , Kyeong Song , Yeonghun Youn","doi":"10.1016/j.na.2024.113559","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate elliptic irregular obstacle problems with <span><math><mi>p</mi></math></span>-growth involving measure data. Emphasis is on the strongly singular case <span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>n</mi></mrow></math></span>, and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive zero-order potential estimates.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Singular elliptic measure data problems with irregular obstacles\",\"authors\":\"Sun-Sig Byun , Kyeong Song , Yeonghun Youn\",\"doi\":\"10.1016/j.na.2024.113559\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate elliptic irregular obstacle problems with <span><math><mi>p</mi></math></span>-growth involving measure data. Emphasis is on the strongly singular case <span><math><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>2</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>n</mi></mrow></math></span>, and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive zero-order potential estimates.</p></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-05-09\",\"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://www.sciencedirect.com/science/article/pii/S0362546X24000786\",\"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://www.sciencedirect.com/science/article/pii/S0362546X24000786","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
我们研究了涉及度量数据的 p 增长的椭圆不规则障碍问题。重点是强奇异情况 1<p≤2-1/n，我们获得了几种新的比较估计值，证明了本征形式的梯度势估计值。我们的方法也可用于推导零阶势能估计。
Singular elliptic measure data problems with irregular obstacles
We investigate elliptic irregular obstacle problems with -growth involving measure data. Emphasis is on the strongly singular case , and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive zero-order potential estimates.
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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