{"title":"A comparison method for the fractional Laplacian and applications","authors":"Alireza Ataei , Alireza Tavakoli","doi":"10.1016/j.aim.2024.109901","DOIUrl":null,"url":null,"abstract":"<div><p>We study the boundary behavior of solutions to fractional Laplacian. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is proved in the bounded open sets with Wiener regular boundary. Then, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for the fractional Laplacian.</p></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"457 ","pages":"Article 109901"},"PeriodicalIF":1.5000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S000187082400416X/pdfft?md5=bff3ab0b576373357ae665081f0d45e1&pid=1-s2.0-S000187082400416X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S000187082400416X","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/8/29 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the boundary behavior of solutions to fractional Laplacian. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is proved in the bounded open sets with Wiener regular boundary. Then, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for the fractional Laplacian.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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