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.

An equivalent path functional formulation of branched transportation problems

BRASCO, Lorenzo;
2011

Abstract

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.
2011
Brasco, Lorenzo; Santambrogio, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2333288
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