preprint

Inserted: 6 dec 2023

Year: 2023

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.