最优域上的边界哈纳克原理

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2021-12-02 DOI:10.2422/2036-2145.202112_003

Francesco Paolo Maiale, Giorgio Tortone, B. Velichkov

{"title":"最优域上的边界哈纳克原理","authors":"Francesco Paolo Maiale, Giorgio Tortone, B. Velichkov","doi":"10.2422/2036-2145.202112_003","DOIUrl":null,"url":null,"abstract":"Abstract. We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"65 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"The Boundary Harnack principle on optimal domains\",\"authors\":\"Francesco Paolo Maiale, Giorgio Tortone, B. Velichkov\",\"doi\":\"10.2422/2036-2145.202112_003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract. We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.\",\"PeriodicalId\":8132,\"journal\":{\"name\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"volume\":\"65 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2422/2036-2145.202112_003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2422/2036-2145.202112_003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 3

摘要

摘要对于一类满足某些几何条件的域，我们给出了边界Harnack不等式的一个简短且完备的证明，该证明是用一个状态函数给出的，该状态函数表现为到边界的距离函数，在域内是次调和的，并且满足对其水平集测度的一些适当估计。我们还讨论了这一结果在某些形状优化和自由边界问题中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The Boundary Harnack principle on optimal domains

Abstract. We give a short and self-contained proof of the Boundary Harnack inequality for a class of domains satisfying some geometric conditions given in terms of a state function that behaves as the distance function to the boundary, is subharmonic inside the domain and satisfies some suitable estimates on the measure of its level sets. We also discuss the applications of this result to some shape optimization and free boundary problems.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

自引率

0.00%

发文量

期刊最新文献

Continued fractions of cubic Laurent series and their effective irrationality exponents Joint normality of representations of numbers: an ergodic approach Rigidity of non-compact static domains in hyperbolic space via positive mass theorems A characterization of chains in dimension three Divides and hyperbolic volumes