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math.AP2013
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…
math.AP2013
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…
math.AP2013
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…