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math.FA2019
Sobolev spaces in extended metric-measure spaces
Giuseppe Savaré
These lecture notes contain an extended version of the material presented in the C.I.M.E. summer course in 2017, aiming to give a detailed introduction to the metric Sobolev theory…
math.AP2019
Contraction and regularizing properties of heat flows in metric measure spaces
Giulia Luise, Giuseppe Savaré
We illustrate some novel contraction and regularizing properties of the Heat flow in metric-measure spaces that emphasize an interplay between Hellinger-Kakutani, Kantorovich-Wasse…