Differential of metric valued Sobolev maps
Gigli, N., Pasqualetto, E., & Soultanis, E. (2020). Differential of metric valued Sobolev maps. Journal of Functional Analysis, 278(6), Article 108403. https://doi.org/10.1016/j.jfa.2019.108403
Published inJournal of Functional Analysis
© 2019 Published by Elsevier Inc
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is R. We also show compatibility with the concept of co-local weak differential introduced by Convent and Van Schaftingen.
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