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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon |
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todo:paper_02132230_v30_n1_p277_Mazon2023-10-03T15:10:06Z An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary Mazón, J.M. Rossi, J.D. Toledo, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Mazón, J.M. Rossi, J.D. Toledo, J. 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. |
| format |
JOUR |
| author |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_facet |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_sort |
Mazón, J.M. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_02132230_v30_n1_p277_Mazon |
| work_keys_str_mv |
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