{"title":"Fractional Hardy–Rellich inequalities via integration by parts","authors":"Nicola De Nitti , Sidy Moctar Djitte","doi":"10.1016/j.na.2023.113478","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a fractional Hardy–Rellich inequality with an explicit constant in bounded domains of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>. The strategy of the proof generalizes an approach pioneered by E. Mitidieri (<em>Mat. Zametki</em>, 2000) by relying on a Pohozaev-type identity.</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"243 ","pages":"Article 113478"},"PeriodicalIF":1.3000,"publicationDate":"2024-03-05","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/S0362546X23002705","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a fractional Hardy–Rellich inequality with an explicit constant in bounded domains of class . The strategy of the proof generalizes an approach pioneered by E. Mitidieri (Mat. Zametki, 2000) by relying on a Pohozaev-type identity.
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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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