An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary

In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the...

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Autor principal: Rossi, Julio Daniel
Publicado: 2014
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Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v30_n1_p277_Mazon
http://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon
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spelling paper:paper_02132230_v30_n1_p277_Mazon2023-06-08T15:20:47Z An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary Rossi, Julio Daniel Mass transport Monge-Kantorovich problems P-Laplacian equation In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the dual problem we find a Kantorovich potential as the limit as p→∞ of solutions to p-Laplacian type problems with nonlinear boundary conditions. In addition, we show that this limit encodes all the relevant information for our problem. It provides the masses that are exported and imported from the boundary and also allows the construction of an optimal transport plan. Finally we show that the arguments can be adapted to deal with the case in which the mass that can be exported/imported is bounded by prescribed functions. © European Mathematical Society. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v30_n1_p277_Mazon http://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon
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
P-Laplacian equation
spellingShingle Mass transport
Monge-Kantorovich problems
P-Laplacian equation
Rossi, Julio Daniel
An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
topic_facet Mass transport
Monge-Kantorovich problems
P-Laplacian equation
description In this paper we analyze a mass transportation problem in a bounded domain in which there is the possibility of import/export mass across the boundary paying a tax in addition to the transport cost that is assumed to be given by the Euclidean distance. We show a general duality argument and for the dual problem we find a Kantorovich potential as the limit as p→∞ of solutions to p-Laplacian type problems with nonlinear boundary conditions. In addition, we show that this limit encodes all the relevant information for our problem. It provides the masses that are exported and imported from the boundary and also allows the construction of an optimal transport plan. Finally we show that the arguments can be adapted to deal with the case in which the mass that can be exported/imported is bounded by prescribed functions. © European Mathematical Society.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
title_short An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
title_full An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
title_fullStr An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
title_full_unstemmed An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
title_sort optimal transportation problem with a cost given by the euclidean distance plus import/export taxes on the boundary
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v30_n1_p277_Mazon
http://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon
work_keys_str_mv AT rossijuliodaniel anoptimaltransportationproblemwithacostgivenbytheeuclideandistanceplusimportexporttaxesontheboundary
AT rossijuliodaniel optimaltransportationproblemwithacostgivenbytheeuclideandistanceplusimportexporttaxesontheboundary
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