288 citations · 1.7k across the 31 of their papers we have counts for
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A Lagrangian approach to totally dissipative evolutions in Wasserstein spaces
Giulia Cavagnari, Giuseppe Savaré, Giacomo Enrico Sodini
We introduce and study the class of totally dissipative multivalued probability vector fields (MPVF) on the Wasserstein space $(\mathcal{P}_2(\mathsf{X}),W…
Extension of monotone operators and Lipschitz maps invariant for a group of isometries
Giulia Cavagnari, Giuseppe Savaré, Giacomo Enrico Sodini
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal ex…
Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces
Massimo Fornasier, Giuseppe Savaré, Giacomo Enrico Sodini
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz functions in the metric-Sobolev space associated wi…
On the duality between p-Modulus and probability measures
Luigi Ambrosio, Simone Di Marino, Giuseppe Savaré
Motivated by recent developments on calculus in metric measure spaces , we prove a general duality principle between Fuglede's notion of -modulus for…
Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces
Giuseppe Savaré
We prove that the linear heat flow in a RCD(K,\infty) metric measure space (X,d,m) satisfies a contraction property with respect to every L^p-Kantorovich-Rubinstein-Wasserstein dis…
Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
The aim of the present paper is to bridge the gap between the Bakry-Émery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature b…