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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
