Differential structure associated to axiomatic Sobolev spaces
Nicola Gigli, Enrico Pasqualetto
TL;DR
This paper explores how axiomatic Sobolev spaces on general metric measure spaces can induce a first-order differential structure when certain locality conditions are met.
Contribution
It clarifies the relationship between axiomatic Sobolev spaces and differential structures in metric measure spaces, extending previous frameworks.
Findings
Axiomatic Sobolev spaces induce differential structures under locality assumptions
Provides a theoretical foundation for differential calculus in metric measure spaces
Connects Sobolev space axioms with geometric and analytical structures
Abstract
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.
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