{"title":"Gagliardo-Nirenberg-Sobolev inequalities on planar graphs","authors":"M. Esteban","doi":"10.3934/cpaa.2022051","DOIUrl":null,"url":null,"abstract":"In this paper we study a family of the interpolation Gagliardo-Nirenberg-Sobolev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. The inequalities being equivalent to some minimization problems, we also analyse the set of solutions of the Euler-Lagrange equations satisfied by extremal functions, or equivalently, by minimizers.","PeriodicalId":435074,"journal":{"name":"Communications on Pure & Applied Analysis","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure & Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cpaa.2022051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper we study a family of the interpolation Gagliardo-Nirenberg-Sobolev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. The inequalities being equivalent to some minimization problems, we also analyse the set of solutions of the Euler-Lagrange equations satisfied by extremal functions, or equivalently, by minimizers.
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