Année 2020-2021

A variational approach to the regularity theory of optimal transport maps

par Maxime Prod'homme

Europe/Paris
À distance

À distance

Description

Once the existence of an optimal transport map between two probability densities has been established, the question of its regularity is very natural. After Caffarelli's first ground-breaking result in the case of a convex target domain, Figalli and Kim proved, working at the level of the convex potential and the Monge-Ampère equation, partial regularity of the optimal transport map for the Euclidean cost, without any convexity assumption. In this talk, I will present a purely variational proof, obtained by Goldman and Otto, of this result and then an extension of this strategy to the case of optimal transport with any reasonable cost, thus providing a variational proof of a result already obtained by De Philippis and Figalli. This is based on a joint work with Felix Otto and Tobias Ried.

Organisé par

Maxime Laborde