Accepted Paper
Inserted: 9 nov 2010
Last Updated: 4 jan 2012
Journal: J. Math. Sci.
Pages: 35
Year: 2010
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.
Keywords: Optimal transport, Branched transport, continuity equation, relativistic heat equation
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