96 citations · 386 across the 22 of their papers we have counts for
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A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations
Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg
Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown…
Monge problem in metric measure spaces with Riemannian curvature-dimension condition
Fabio Cavalletti
We prove the existence of solutions for the Monge minimization problem, addressed in a metric measure space enjoying the Riemannian curvature-dimension condition $\RCD(K,…
A note on a residual subset of Lipschitz functions on metric spaces
Fabio Cavalletti
Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero poi…
The Polar Cone of the set of monotone maps
Fabio Cavalletti, Michael Westdickenberg
We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the posi…
Existence and uniqueness of optimal transport maps
Fabio Cavalletti, Martin Huesmann
Let be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex fu…