{"title":"带低阶余项的扭曲尖锐索波列夫不等式的极值函数。高维情况","authors":"Olivier Druet, Emmanuel Hebey, Frédéric Robert","doi":"10.1515/crelle-2024-0056","DOIUrl":null,"url":null,"abstract":"\n <jats:p>We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 𝑛-dimensional Sobolev inequalities with lower order remainder terms when <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mi>n</m:mi>\n <m:mo>≥</m:mo>\n <m:mn>5</m:mn>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0056_ineq_0001.png\"/>\n <jats:tex-math>n\\geq 5</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>.</jats:p>","PeriodicalId":508691,"journal":{"name":"Journal für die reine und angewandte Mathematik (Crelles Journal)","volume":"13 12","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms. The high-dimensional case\",\"authors\":\"Olivier Druet, Emmanuel Hebey, Frédéric Robert\",\"doi\":\"10.1515/crelle-2024-0056\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n <jats:p>We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 𝑛-dimensional Sobolev inequalities with lower order remainder terms when <jats:inline-formula>\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:mrow>\\n <m:mi>n</m:mi>\\n <m:mo>≥</m:mo>\\n <m:mn>5</m:mn>\\n </m:mrow>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_crelle-2024-0056_ineq_0001.png\\\"/>\\n <jats:tex-math>n\\\\geq 5</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula>.</jats:p>\",\"PeriodicalId\":508691,\"journal\":{\"name\":\"Journal für die reine und angewandte Mathematik (Crelles Journal)\",\"volume\":\"13 12\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal für die reine und angewandte Mathematik (Crelles Journal)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/crelle-2024-0056\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal für die reine und angewandte Mathematik (Crelles Journal)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/crelle-2024-0056","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了当 n ≥ 5 n\geq 5 时，具有低阶余项的扭曲尖锐𝑛维 Sobolev 不等式的极值函数的存在性和极值函数集的紧凑性。
Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms. The high-dimensional case
We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 𝑛-dimensional Sobolev inequalities with lower order remainder terms when n≥5n\geq 5.
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