6533b82efe1ef96bd1292a2b

RESEARCH PRODUCT

Differential of metric valued Sobolev maps

Enrico PasqualettoElefterios SoultanisNicola Gigli

subject

metric measure spacesPure mathematicsFunction spaces; Metric measure spaces; Sobolev spaces01 natural sciencesMetric measure spacesfunction spacesSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: MathematicsTrigonometric functions0101 mathematicsMathematicsEuclidean space010102 general mathematicsTangentmetriset avaruudetFunctional Analysis (math.FA)Mathematics - Functional AnalysisSobolev spaceMetric spaceSobolev spacesFunction spaces010307 mathematical physicsfunktionaalianalyysiMetric differentialAnalysis

description

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 $\mathbb{R}$.

yearjournalcountryeditionlanguage
2020-01-01Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2019.108403