Sobolev mappings: Lipschitz density is not an isometric invariant of the target

Details Sobolev mappings: Lipschitz density is not an isometric invariant of the target Sobolev mappings: Lipschitz density is not an isometric invariant of the target

2011-09-21

arxiv.org/abs/1109.4614v1

Int. Math. Res. Not. IMRN Vol. 2011, no.12, 2794-2809

Mathematics

Functional Analysis

Scientific paper

10.1093/imrn/rnq183

If $M$ is a compact smooth manifold and $X$ is a compact metric space, the
Sobolev space $W^{1,p}(M,X)$ is defined through an isometric embedding of $X$
into a Banach space. We prove that the answer to the question whether Lipschitz
mappings ${\rm Lip}\,(M,X)$ are dense in $W^{1,p}(M,X)$ may depend on the
isometric embedding of the target.

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