Differential structure associated to axiomatic Sobolev spaces

2018/07/14 by Gigli, Nicola, Pasqualetto, Enrico
#46E35 #51Fxx #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1807.05417

Abstract

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.

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