Optimal matching problems with costs given by Finsler distances

J. M. Mazón; Julio D. Rossi; J. Toledo

doi:10.3934/cpaa.2015.14.229

Article Contents

2015, Volume 14, Issue 1: 229-244. Doi: 10.3934/cpaa.2015.14.229

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Optimal matching problems with costs given by Finsler distances

1.
Departament d'Anàlisi Matemàtica, U. de València, Valencia
2.
Departamento de Análisis Matemático, Universidad de Alicante, Ap 99, 03080, Alicante

Received: December 31, 2013

Revised: March 31, 2014

Published: December 2014

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Abstract

In this paper we deal with an optimal matching problem, that is, we want to transport two commodities (modeled by two measures that encode the spacial distribution of each commodity) to a given location, where they will match, minimizing the total transport cost that in our case is given by the sum of the two different Finsler distances that the two measures are transported. We perform a method to approximate the matching measure and the pair of Kantorovich potentials associated with this problem taking limit as $p\to \infty$ in a variational system of $p-$Laplacian type.

Keywords:

Optimal matching problem,
MongeKantorovichs mass transport theory,
$p$Laplacian systems.

Mathematics Subject Classification: Primary: 49J20, 35J92.

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