{"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":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"245 ","pages":"Article 113559"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000786","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/9 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
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.
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Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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