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引用次数: 0
摘要
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。
On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains
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.
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.