{"title":"On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains","authors":"Winfried Sickel","doi":"10.1134/s0081543823050085","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Let <span>\\(E\\)</span> be a domain in <span>\\(\\mathbb R^d\\)</span>. We investigate the regularity of the characteristic function <span>\\(\\mathcal X_E\\)</span> depending on the behavior of the <span>\\(\\delta\\)</span>-neighborhoods of the boundary of <span>\\(E\\)</span>. The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"72 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823050085","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let \(E\) be a domain in \(\mathbb R^d\). We investigate the regularity of the characteristic function \(\mathcal X_E\) depending on the behavior of the \(\delta\)-neighborhoods of the boundary of \(E\). The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces.
Abstract Let \(E\) be a domain in \(\mathbb R^d\).我们研究了特征函数 \(\mathcal X_E\) 的正则性，它取决于 \(E\) 边界的 \(\delta\)-neighborhoods 的行为。正则性是通过尼克尔斯基-贝索夫空间和利佐金-特里贝尔空间来衡量的。
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
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