{"title":"Higher integrability of the gradient for the thermal insulation problem","authors":"Camille Labourie, Emmanouil Milakis","doi":"10.4171/ifb/481","DOIUrl":null,"url":null,"abstract":"We prove the higher integrability of the gradient for local minimizers of the thermal insulation problem, an analogue of De Giorgi’s conjecture for the Mumford-Shah functional. We deduce that the singular part of the free boundary has Hausdorff dimension strictly less than n− 1. AMS Subject Classifications: 35R35, 35J20, 49N60, 49Q20.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"65 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Interfaces and Free Boundaries","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ifb/481","RegionNum":4,"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
We prove the higher integrability of the gradient for local minimizers of the thermal insulation problem, an analogue of De Giorgi’s conjecture for the Mumford-Shah functional. We deduce that the singular part of the free boundary has Hausdorff dimension strictly less than n− 1. AMS Subject Classifications: 35R35, 35J20, 49N60, 49Q20.
期刊介绍：
Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.
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