6 papers
A study of the metric measure space of probability measures via a purely atomic superposition principle
Alessandro Pinzi
We study the continuity equation on the metric measure space , when is either the Euclidean space or a compact, oriented, and boundaryless Riemannian…
Optimal transport between laws of random probability measures and the strict Monge problem
Alessandro Pinzi
We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that…
A direct method for doubly nonlinear equations via convexification in spaces of measures and duality
Alessandro Pinzi, Filippo Riva, Giuseppe Savaré
Existence of solutions to doubly nonlinear equations in reflexive Banach spaces is established by resorting to a global-in-time variational approach inspired by De Giorgi's princip…
Nested superposition principle for random measures and the geometry of the Wasserstein on Wasserstein space
Alessandro Pinzi, Giuseppe Savaré
We study the geometric structure of the space of random measures , endowed with the Wasserstein on Wasserstein metric, where is a complete…
First order equation on random measures as superposition of weak solutions to the McKean-Vlasov equation
Alessandro Pinzi
The goal of this paper is to define an evolution equation for a curve of random probability measures associated to…
Totally convex functions, -Optimal transport for laws of random measures, and solution to the Monge problem
Alessandro Pinzi, Giuseppe Savaré
We study the Optimal Transport problem for laws of random measures in the Kantorovich-Wasserstein space , associated with a Hilbert space…