Calculus of Variations and Geometric Measure Theory
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N. Gigli - E. Pasqualetto - E. Soultanis

Differential of metric valued Sobolev maps

created by pasqualetto on 26 Jul 2018

[BibTeX]

Submitted Paper

Inserted: 26 jul 2018
Last Updated: 26 jul 2018

Year: 2018

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 $\mathbb{R}$.

Keywords: Function spaces, Metric measure spaces, Sobolev spaces


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