Calculus of Variations and Geometric Measure Theory

F. Santambrogio

A Dacorogna-Moser approach to flow decomposition and minimal flow problems

created by santambro on 10 Oct 2013
modified on 26 Sep 2014


Accepted Paper

Inserted: 10 oct 2013
Last Updated: 26 sep 2014

Year: 2014

This paper will be published in the proceedings of the national conference of SMAI (the French Applied Math Society) of May 2013.


The papers describes an easy approach, based on a classical construction by Dacorogna and Moser, to prove that optimal vector fields in some minimal flow problem linked to optimal transport models (congested traffic, branched transport, Beckmann's problem\dots) are induced by a probability measure on the space of paths. This gives a new, easier, proof of a classical result by Smirnov, and allows handling optimal flows without taking care of the presence of cycles.