14 citations · 19 across the 15 of their papers we have counts for
9 papers · 1 filter
Approximation in Metric Sobolev Spaces: A General Framework
Massimo Fornasier, Giacomo Enrico Sodini
In our recent work [FHS25], we introduced a numerical framework for approximating Sobolev functions on Wasserstein spaces from finite samples, leveraging structural properties esta…
Stochastic Euler Schemes and Dissipative Evolutions in the Space of Probability Measures
Giulia Cavagnari, Giuseppe Savaré, Giacomo Enrico Sodini
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and…
Evolution variational inequalities with general costs
Pierre-Cyril Aubin-Frankowski, Giacomo Enrico Sodini, Ulisse Stefanelli
We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions , including Bregman and entrop…
The Hellinger-Kantorovich metric measure geometry on spaces of measures
Lorenzo Dello Schiavo, Giacomo Enrico Sodini
Let be a Riemannian manifold with Riemannian distance , and be the space of all non-negative Borel measures on , endowed with the Hellinge…
Functions of bounded variation and Lipschitz algebras in metric measure spaces
Enrico Pasqualetto, Giacomo Enrico Sodini
Given a unital algebra of locally Lipschitz functions defined over a metric measure space , we study two associated notions of f…
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…
The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities
Giacomo Enrico Sodini
We show that the algebra of cylinder functions in the Wasserstein Sobolev space generated by a finite and po…
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…