A characterization of the subspace of radially symmetric functions in Sobolev spaces
arXiv:2209.02286 · doi:10.1142/S0219199724500184
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.
12 pages, revised and restructured to match the published version. Section 1 and 2 have been expanded and improved, Theorem 1 in v1 has been split into Theorems 1.1 and 1.2, an application to Sobolev norms of corotational maps has been added in Theorem 1.3, references have been updated