索波列夫空间中径向对称函数子空间的表征

IF 1.2 2区数学 Q1 MATHEMATICS

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

Matthias Ostermann

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引用次数: 0

摘要

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

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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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.