{"title":"p = 1的Caffarelli-Kohn-Nirenberg型不等式的径向对称及其破缺","authors":"N. Chiba, T. Horiuchi","doi":"10.5036/MJIU.47.49","DOIUrl":null,"url":null,"abstract":"The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and isoperimetric inequalities with weights. 1. We show that symmetry breaking occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the CKN-type inequalities with p = 1 and isoperimetric inequalities with weights.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"58 1","pages":"49-63"},"PeriodicalIF":0.0000,"publicationDate":"2016-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1\",\"authors\":\"N. Chiba, T. Horiuchi\",\"doi\":\"10.5036/MJIU.47.49\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and isoperimetric inequalities with weights. 1. We show that symmetry breaking occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the CKN-type inequalities with p = 1 and isoperimetric inequalities with weights.\",\"PeriodicalId\":18362,\"journal\":{\"name\":\"Mathematical Journal of Ibaraki University\",\"volume\":\"58 1\",\"pages\":\"49-63\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Journal of Ibaraki University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/MJIU.47.49\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Journal of Ibaraki University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/MJIU.47.49","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On radial symmetry and its breaking in the Caffarelli-Kohn-Nirenberg type inequalities for p = 1
The main purpose of this article is to study the Caffarelli-Kohn-Nirenberg type inequalities (1.2) with p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the Caffarelli-Kohn-Nirenberg type inequalities with p = 1 and isoperimetric inequalities with weights. 1. We show that symmetry breaking occurs provided that a parameter j (cid:13) j is large enough. In the argument we effectively employ equivalence between the CKN-type inequalities with p = 1 and isoperimetric inequalities with weights.
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