A characterization of the subspace of radially symmetric functions in Sobolev spaces

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2024-05-07 DOI:10.1142/s0219199724500184

Matthias Ostermann

引用次数: 0

Abstract

In this paper, we show that any Sobolev norm of nonnegative integer order of radially symmetric functions is equivalent to a weighted Sobolev norm of their radial profile. This establishes in terms of weighted Sobolev spaces on an interval a complete characterization of radial Sobolev spaces, which was open until now. As an application, we give a description of Sobolev norms of corotational maps.

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索波列夫空间中径向对称函数子空间的表征

在本文中，我们证明了任何径向对称函数的非负整数阶 Sobolev 准则等价于其径向剖面的加权 Sobolev 准则。这就用区间上的加权 Sobolev 空间建立了径向 Sobolev 空间的完整表征，而这一表征直到现在仍是开放的。作为一个应用，我们给出了冠状映射的索波列夫规范的描述。

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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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.