Calculus of Variations and Geometric Measure Theory

L. Brasco - F. Santambrogio

An equivalent path functional formulation of branched transportation problems

created by brasco on 25 Nov 2009
modified on 23 Mar 2010


Accepted Paper

Inserted: 25 nov 2009
Last Updated: 23 mar 2010

Journal: Discrete Contin. Dyn. Syst.
Year: 2010


We consider two models for branched transport: the one introduced in Bernot et al. (Publ Mat 49:417-451, 2005), which makes use of a functional defined on measures over the space of Lipschitz paths, and the path functional model presented in Brancolini et al. (J Eur Math Soc 8:415-434, 2006), where one minimizes some suitable action functional defined over the space of measure-valued Lipschitz curves, getting sort of a Riemannian metric on the space of probabilities, favouring atomic measures, with a cost depending on the masses of each of their atoms. We prove that modifying the latter model according to Brasco (Ann Mat Pura Appl 189:95-125, 2010), then the two models turn out to be equivalent.

Keywords: Branched transport, Irrigation patterns, Path functionals