552 citations · 841 across the 12 of their papers we have counts for
13 papers
Visco-energetic solutions for a model of crack growth in brittle materials
Gianni Dal Maso, Riccarda Rossi, Giuseppe Savaré +1
Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced…
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…
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…
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
Luigi Ambrosio, Matthias Erbar, Giuseppe Savaré
We introduce the setting of extended metric-topological measure spaces as a general "Wiener-like" framework for optimal transport problems and nonsmooth metric analysis in infinite…
Balanced-Viscosity solutions for multi-rate systems
Alexander Mielke, Riccarda Rossi, Giuseppe Savaré
Several mechanical systems are modeled by the static momentum balance for the displacement coupled with a rate-independent flow rule for some internal variable . We consider…
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Nicola Gigli, Andrea Mondino, Giuseppe Savaré
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equi…