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math.FA2018
Differential of metric valued Sobolev maps
Nicola Gigli, Enrico Pasqualetto, Elefterios Soultanis
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,…
math.FA2018
Differential structure associated to axiomatic Sobolev spaces
Nicola Gigli, Enrico Pasqualetto
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 assum…