Gigli, Nicola Pasqualetto, Enrico Soultanis, Elefterios 2019-11-13 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. application/pdf https://folia.unifr.ch/global/documents/308435 https://folia.unifr.ch/documents/308435/files/sou_dmv.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jfa.2019.108403 info:eu-repo/semantics/openAccess License undefined Journal of Functional Analysis. - 2020, vol. 278, no. 6, p. 108403 info:eu-repo/classification/udc/51 Differential of metric valued Sobolev maps http://purl.org/coar/resource_type/c_6501