14 citations · 19 across the 15 of their papers we have counts for
18 papers
A Lagrangian superposition principle for the continuity equation with reaction
Stefano Almi, Giacomo Enrico Sodini
We study the continuity equation with reaction on , driven by Borel velocity and reaction fields and . We…
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…
The Brezis-Ekeland-Nayroles principle in metric spaces: time-continuous setting
Pierre-Cyril Aubin-Frankowski, Giacomo Enrico Sodini, Ulisse Stefanelli
Based on a variational characterization of the local slope of a functional, we extend the celebrated Brezis-Ekeland-Nayroles null-minimization principle to curves of maximal slope…
HJB equations driven by the Dirichlet-Ferguson Laplacian in Wasserstein-Sobolev spaces
François Delarue, Mattia Martini, Giacomo Enrico Sodini
We study linear and nonlinear PDEs defined on the space of over the flat torus , equipped with the Dirichlet-Ferguson measure $\mathcal{D}…
Global well-posedness for a time-fractional doubly nonlinear equation
Goro Akagi, Giacomo Enrico Sodini, Ulisse Stefanelli
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearit…
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 infimal convolution structure of the Hellinger-Kantorovich distance
Nicolò De Ponti, Giacomo Enrico Sodini, Luca Tamanini
We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke,…
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 relaxation viewpoint to Unbalanced Optimal Transport: duality, optimality and Monge formulation
Giuseppe Savaré, Giacomo Enrico Sodini
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. Thes…
Approximation Theory, Computing, and Deep Learning on the Wasserstein Space
Massimo Fornasier, Pascal Heid, Giacomo Enrico Sodini
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical…
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…
Dissipative probability vector fields and generation of evolution semigroups in Wasserstein spaces
Giulia Cavagnari, Giuseppe Savaré, Giacomo Enrico Sodini
We introduce and investigate a notion of multivalued -dissipative probability vector field (MPVF) in the Wasserstein space of Borel probability measur…
Numerical Methods for a System of Coupled Cahn-Hilliard Equations
Mattia Martini, Giacomo Enrico Sodini
In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are base…