A1 Journal article (refereed)
Differential of metric valued Sobolev maps (2020)

Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (2020). Differential of metric valued Sobolev maps. Journal of Functional Analysis, 278 (6), 108403. DOI: 10.1016/j.jfa.2019.108403

JYU authors or editors

Publication details

All authors or editors: Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios

Journal or series: Journal of Functional Analysis

ISSN: 0022-1236

eISSN: 1096-0783

Publication year: 2020

Volume: 278

Issue number: 6

Article number: 108403

Publisher: Elsevier

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jfa.2019.108403

Open Access: Publication channel is not openly available

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1807.10063

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.

Keywords: functional analysis; metric spaces

Free keywords: function spaces; metric measure spaces; Sobolev spaces

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 2