Calculus of Variations and Geometric Measure Theory

G. Buttazzo

Evolution models for mass transportation problems

created by buttazzo on 07 Apr 2012


Accepted Paper

Inserted: 7 apr 2012
Last Updated: 7 apr 2012

Journal: Milan J. Math.
Year: 2012

Milan J. Math., (to appear), DOI: 10.1007s00032-012-0175-x


We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in 5, where a suitable cost functional $F(\rho,v)$, depending on the density $\rho$ and on the velocity $v$ (which fulfill the continuity equation), has to be minimized. Acting on the functional $F$ various forms of mass transportation problems can be modeled, as for instance those presenting congestion effects, occurring in traffic simulations and in crowd motions, or concentration effects, which give rise to branched structures.

Keywords: Optimal transport, Branched transport, continuity equation, functionals on measures, congested transport