14 citations · 19 across the 15 of their papers we have counts for
4 papers · 1 filter
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}…
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…
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…