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arXiv · 2209.02286

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

Matthias Ostermann
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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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BibTeXRIS

Matthias Ostermann. 2022-09-06. A characterization of the subspace of radially symmetric functions in Sobolev spaces. https://doi.org/10.1142/s0219199724500184

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