{"title":"The Poisson equation involving surface measures","authors":"Marius Müller","doi":"10.1080/03605302.2021.2013882","DOIUrl":null,"url":null,"abstract":"Abstract We prove the (optimal) -regularity of weak solutions to the equation in a domain with Dirichlet boundary conditions, where is a compact (Lipschitz) manifold and We also discuss optimality and necessity of the assumptions on Q and Γ. Our findings can be applied to study the regularity of solutions for several free boundary problems, in particular the biharmonic Alt–Caffarelli problem.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"948 - 988"},"PeriodicalIF":1.7000,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2021.2013882","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We prove the (optimal) -regularity of weak solutions to the equation in a domain with Dirichlet boundary conditions, where is a compact (Lipschitz) manifold and We also discuss optimality and necessity of the assumptions on Q and Γ. Our findings can be applied to study the regularity of solutions for several free boundary problems, in particular the biharmonic Alt–Caffarelli problem.
期刊介绍：
This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.
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