约束下改进的Sobolev不等式

arXiv: Classical Analysis and ODEs Pub Date : 2020-10-20 DOI:10.1093/IMRN/RNAB067

Fengbo Hang, Xiaodong Wang

{"title":"约束下改进的Sobolev不等式","authors":"Fengbo Hang, Xiaodong Wang","doi":"10.1093/IMRN/RNAB067","DOIUrl":null,"url":null,"abstract":"We give a new proof of Aubin's improvement of the Sobolev inequality on $\\mathbb{S}^{n}$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on $\\mathbb{S}^{n}$, we determine the constant explicitly in the second order moments case.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Improved Sobolev Inequality Under Constraints\",\"authors\":\"Fengbo Hang, Xiaodong Wang\",\"doi\":\"10.1093/IMRN/RNAB067\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a new proof of Aubin's improvement of the Sobolev inequality on $\\\\mathbb{S}^{n}$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on $\\\\mathbb{S}^{n}$, we determine the constant explicitly in the second order moments case.\",\"PeriodicalId\":8451,\"journal\":{\"name\":\"arXiv: Classical Analysis and ODEs\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/IMRN/RNAB067\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/IMRN/RNAB067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 6

摘要

在$\mathbb{S}^{n}$上给出了Aubin对Sobolev不等式的改进，在面积元的一阶矩消失的情况下给出了新的证明，并将其推广到高阶矩的情况。通过对$\mathbb{S}^{n}$上的一个极值问题的仔细研究，我们明确地确定了二阶矩情况下的常数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Improved Sobolev Inequality Under Constraints

We give a new proof of Aubin's improvement of the Sobolev inequality on $\mathbb{S}^{n}$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on $\mathbb{S}^{n}$, we determine the constant explicitly in the second order moments case.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Classical Analysis and ODEs

自引率

0.00%

发文量