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 $c(x,y)=|x-y|^2$. 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.

A survey on dynamical transport distances

BRASCO, Lorenzo
2012

Abstract

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 $c(x,y)=|x-y|^2$. 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.
2012
Brasco, Lorenzo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2333290
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