Weak differentiability of metric space valued Sobolev maps
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.17303
 arXiv:
 arXiv:2303.17303
 Bibcode:
 2023arXiv230317303C
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 46E36;
 46B25
 EPrint:
 14 pages