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arXiv · 2303.17303

Weak differentiability of metric space valued Sobolev maps

Paul Creutz·Nikita Evseev
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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.

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Paul Creutz, Nikita Evseev. 2023-03-30. Weak differentiability of metric space valued Sobolev maps. https://arxiv.org/abs/2303.17303

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