{"title":"通过分部积分的分数哈代-雷利希不等式","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":"{\"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}","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
摘要
我们证明了在类 C1,1 有界域中具有明确常数的分数哈代-雷利克不等式。证明策略是对 E. Mitidieri(Mat. Zametki, 2000)开创的一种方法的推广,它依赖于 Pohozaev 类型的特性。
Fractional Hardy–Rellich inequalities via integration by parts
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.
期刊介绍:
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