{"title":"Some properties of the torsion function with Robin boundary conditions","authors":"Rossano Sannipoli","doi":"10.4171/rlm/962","DOIUrl":null,"url":null,"abstract":"In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\\infty}$ and $L^p$ norms, for $p\\ge 1$, of the torsion function, seen as a functional on a bounded simply connected domain $\\Omega \\in \\mathbb{R}^n$, and prove that the balls are a critical shape for these functionals, when the volume is preserved.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti Lincei-Matematica e Applicazioni","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rlm/962","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\infty}$ and $L^p$ norms, for $p\ge 1$, of the torsion function, seen as a functional on a bounded simply connected domain $\Omega \in \mathbb{R}^n$, and prove that the balls are a critical shape for these functionals, when the volume is preserved.
期刊介绍:
The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.