The optimal partial transport problem

Alessio Figalli
Université de Nice Sophia Antipolis

In this talk I will describe a variant of the classical optimal transport problem where, given two densities of mass f and g, one considers the problem of transporting a fixed fraction of the mass of f onto g as cheaply as possible. First, I will show some existence and uniqueness results. Then we will see that this problem corresponds to a Monge-Ampere equation in a domain with free boundary, and we will study the regularity property of the optimal transport map and the free boundary.

Back to Workshop II: Numerics and Dynamics for Optimal Transport