Abstract
Several different approaches to the theory of weakly differentiable functions over abstract metric measure spaces made their appearance in the literature throughout the last twenty years. Amongst them, we shall mainly follow the one (based upon the concept of test plan) that has been proposed by Ambrosio, Gigli and Savaré. The whole Sect. 2.1 is devoted to the definition of such notion of Sobolev space W 1, 2(X) and to its most important properties.
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Gigli, N., Pasqualetto, E. (2020). Sobolev Calculus on Metric Measure Spaces. In: Lectures on Nonsmooth Differential Geometry. SISSA Springer Series, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-030-38613-9_2
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DOI: https://doi.org/10.1007/978-3-030-38613-9_2
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