6 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…
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…
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…
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…
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…