Differential structure associated to axiomatic Sobolev spaces

Research paper by Nicola Gigli, Enrico Pasqualetto

Indexed on: 14 Jul '18Published on: 14 Jul '18Published in: arXiv - Mathematics - Functional Analysis


The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (\`a la Gol'dshtein-Troyanov) induces - under suitable locality assumptions - a first-order differential structure.