{"title":"Sobolev不等式的Sharp梯度稳定性","authors":"A. Figalli, Y. Zhang","doi":"10.1215/00127094-2022-0051","DOIUrl":null,"url":null,"abstract":"Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29, 18, 10, 6, 7, 11, 13, 19, 23, 35, 26, 5, 14, 16, 17, 20, 25, 30, 31, 24, 33, 34], as well as the survey papers [15, 26, 17]. Following this line of research, in this paper we shall investigate the stability of minimizers to the classical Sobolev inequality.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2020-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"39","resultStr":"{\"title\":\"Sharp gradient stability for the Sobolev inequality\",\"authors\":\"A. Figalli, Y. Zhang\",\"doi\":\"10.1215/00127094-2022-0051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29, 18, 10, 6, 7, 11, 13, 19, 23, 35, 26, 5, 14, 16, 17, 20, 25, 30, 31, 24, 33, 34], as well as the survey papers [15, 26, 17]. Following this line of research, in this paper we shall investigate the stability of minimizers to the classical Sobolev inequality.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2020-03-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"39\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2022-0051\",\"RegionNum\":1,\"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":"Duke Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2022-0051","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Sharp gradient stability for the Sobolev inequality
Motivated by important applications to problems in the calculus of variations and evolution PDEs, in recent years there has been a growing interest around the understanding of quantitative stability for functional/geometric inequalities, see for instance [3, 2, 8, 27, 28, 21, 9, 22, 29, 18, 10, 6, 7, 11, 13, 19, 23, 35, 26, 5, 14, 16, 17, 20, 25, 30, 31, 24, 33, 34], as well as the survey papers [15, 26, 17]. Following this line of research, in this paper we shall investigate the stability of minimizers to the classical Sobolev inequality.
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