A Monge-Kantorovich mass transport problem for a discrete distance

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This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to tra...

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Autores principales: Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J.
Formato: JOUR
Materias:
Mass transport
Monge-Kantorovich problems
Nonlocal problems
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00221236_v260_n12_p3494_Igbida
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00221236_v260_n12_p3494_Igbida2023-10-03T14:27:15Z A Monge-Kantorovich mass transport problem for a discrete distance Igbida, N. Mazón, J.M. Rossi, J.D. Toledo, J. Mass transport Monge-Kantorovich problems Nonlocal problems This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans-Gangbo for the classical problem. © 2011 Elsevier Inc. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v260_n12_p3494_Igbida
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Mass transport
Monge-Kantorovich problems
Nonlocal problems
spellingShingle Mass transport
Monge-Kantorovich problems
Nonlocal problems
Igbida, N.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
A Monge-Kantorovich mass transport problem for a discrete distance
topic_facet Mass transport
Monge-Kantorovich problems
Nonlocal problems
description This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans-Gangbo for the classical problem. © 2011 Elsevier Inc.
format JOUR
author Igbida, N.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
author_facet Igbida, N.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
author_sort Igbida, N.
title A Monge-Kantorovich mass transport problem for a discrete distance
title_short A Monge-Kantorovich mass transport problem for a discrete distance
title_full A Monge-Kantorovich mass transport problem for a discrete distance
title_fullStr A Monge-Kantorovich mass transport problem for a discrete distance
title_full_unstemmed A Monge-Kantorovich mass transport problem for a discrete distance
title_sort monge-kantorovich mass transport problem for a discrete distance
url http://hdl.handle.net/20.500.12110/paper_00221236_v260_n12_p3494_Igbida
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