Weak differentiability of metric space valued Sobolev maps
Functional Analysis
2023-03-31 v1 Metric Geometry
Abstract
We show that Sobolev maps with values in a dual Banach space can be characterized in terms of weak derivatives in a weak* sense. Since every metric space embeds isometrically into a dual Banach space, this implies a characterization of metric space valued Sobolev maps in terms of such derivatives. Furthermore, we investigate for which target spaces Sobolev maps are weak* differentiable almost everywhere.
Cite
@article{arxiv.2303.17303,
title = {Weak differentiability of metric space valued Sobolev maps},
author = {Paul Creutz and Nikita Evseev},
journal= {arXiv preprint arXiv:2303.17303},
year = {2023}
}
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14 pages