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.
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Rajala, Tapio (Springer, 2021)We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
Le Donne, Enrico; Rajala, Tapio; Walsberg, Erik (American Mathematical Society, 2018)We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional ...
Di Marino, Simone; Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (Springer, 2021)We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space ...
Giglia, Nicola; Pasqualetto, Enrico (Elsevier GmbH, Urban und Fischer, 2020)The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.
Arroyo, Ángel; Llorente, José G. (American Mathematical Society, 2019)A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we ...