On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains

Pub Date : 2024-03-06 DOI:10.1134/s0081543823050085

Winfried Sickel

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.

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论弱外厚域特征函数的规律性

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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