{"title":"Concentration analysis for elliptic critical equations with no boundary control: Ground-state blow-up","authors":"Hussein Mesmar, Frédéric Robert","doi":"10.3934/dcdss.2023199","DOIUrl":null,"url":null,"abstract":"We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume $ L^2- $concentration. We also analyze the effect of a non-homogeneous nonlinearity that results in the fast convergence of the concentration point.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":"16 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series S","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcdss.2023199","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume $ L^2- $concentration. We also analyze the effect of a non-homogeneous nonlinearity that results in the fast convergence of the concentration point.
期刊介绍：
Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.
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