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.

Differential of metric valued Sobolev maps / Gigli, N.; Pasqualetto, E.; Soultanis, E.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 278:6(2020), pp. 1-18. [10.1016/j.jfa.2019.108403]

Differential of metric valued Sobolev maps

Gigli N.
;
Pasqualetto E.;Soultanis E.
2020

Abstract

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.
278
6
1
18
108403
https://www.sciencedirect.com/science/article/pii/S0022123619303970?via=ihub
https://arxiv.org/abs/1807.10063v1
Gigli, N.; Pasqualetto, E.; Soultanis, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/111340
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