Calculus of Variations and Geometric Measure Theory

L. Brasco

A survey on dynamical transport distances

created by brasco on 09 Nov 2010
modified on 04 Jan 2012


Accepted Paper

Inserted: 9 nov 2010
Last Updated: 4 jan 2012

Journal: J. Math. Sci.
Pages: 35
Year: 2010


In this paper we review some transport models based on the continuity equation, starting with the so-called {\it Benamou-Brenier formula}, which is nothing but a fluid mechanics reformulation of the Monge-Kantorovich problem with cost $c(x,y)=
^2$. We discuss some of its applications (gradient flows, sharp functional inequalities...), as well as some variants and generalizations to dynamical transport problems, where interaction effects among mass particles are considered.

Keywords: Optimal transport, Branched transport, continuity equation, relativistic heat equation