On optimal matching measures for matching problems related to the euclidean distance

We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported...

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Detalles Bibliográficos
Autores principales:	Mazón, J.M., Rossi, J.D., Toledo, J.
Formato:	JOUR
Materias:	Mass transport Monge-Kantorovich problem P-Laplacian equation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_08627959_v139_n4_p553_Mazon
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_08627959_v139_n4_p553_Mazon
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spelling	todo:paper_08627959_v139_n4_p553_Mazon2023-10-03T15:40:17Z On optimal matching measures for matching problems related to the euclidean distance Mazón, J.M. Rossi, J.D. Toledo, J. Mass transport Monge-Kantorovich problem P-Laplacian equation We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p-Laplacian system. We prove that any optimal matching measure for this problem is supported on the boundary of the target set when the two multiples that affect the Euclidean distances involved in the cost are different. Moreover, we present simple examples showing uniqueness or non-uniqueness of the optimal measure. 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_08627959_v139_n4_p553_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 problem P-Laplacian equation
spellingShingle	Mass transport Monge-Kantorovich problem P-Laplacian equation Mazón, J.M. Rossi, J.D. Toledo, J. On optimal matching measures for matching problems related to the euclidean distance
topic_facet	Mass transport Monge-Kantorovich problem P-Laplacian equation
description	We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p-Laplacian system. We prove that any optimal matching measure for this problem is supported on the boundary of the target set when the two multiples that affect the Euclidean distances involved in the cost are different. Moreover, we present simple examples showing uniqueness or non-uniqueness of the optimal measure.
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	On optimal matching measures for matching problems related to the euclidean distance
title_short	On optimal matching measures for matching problems related to the euclidean distance
title_full	On optimal matching measures for matching problems related to the euclidean distance
title_fullStr	On optimal matching measures for matching problems related to the euclidean distance
title_full_unstemmed	On optimal matching measures for matching problems related to the euclidean distance
title_sort	on optimal matching measures for matching problems related to the euclidean distance
url	http://hdl.handle.net/20.500.12110/paper_08627959_v139_n4_p553_Mazon
work_keys_str_mv	AT mazonjm onoptimalmatchingmeasuresformatchingproblemsrelatedtotheeuclideandistance AT rossijd onoptimalmatchingmeasuresformatchingproblemsrelatedtotheeuclideandistance AT toledoj onoptimalmatchingmeasuresformatchingproblemsrelatedtotheeuclideandistance
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On optimal matching measures for matching problems related to the euclidean distance

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