Calculus of Variations and Geometric Measure Theory

Optimal transport with relativistic cost: continuity and Kantorovich potentials for generic cost functions

Jean Louet

created by gelli on 18 Oct 2015
modified by louet on 22 Oct 2015

11 nov 2015 -- 17:00   [open in google calendar]

Aula Seminari Dipartimento di Matematica di Pisa


The optimal transport problem consists in minimizing the total energy of the displacement among all the (vector-valued) functions having prescribed image measure. In this talk we are interested in a particular case of cost functions: $c$ is given by $h(y-x)$ where h is convex, has a bounded domain and is bounded on this domain. The fact that it takes infinite value makes, in particular, complicated the existence of solutions for the dual problem. The strategy consists in introducing a "time-parameter" $t>0$ and in studying the re-scaled problem, with cost $h((y-x)/t)$. We show the continuity of the total cost with respect to $t$, and the existence of Kantorovich potentials for "supercritical" time. This is a joint work with A.Pratelli and F.Zeisler (Erlangen).