An optimal matching problem with constraints

We deal with an optimal matching problem with constraints, that is, we want to transport two measures with the same total mass in RN to a given place (the target set), where they will match and in which we have constraints on the amount of matter we can take to points in the target set. This transpo...

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Detalles Bibliográficos
Autores principales:	Mazón, J.M., Rossi, J.D., Toledo, J.
Formato:	JOUR
Materias:	Mass transport theory Matching problems p-Laplacian equation
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_11391138_v31_n2_p407_Mazon
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_11391138_v31_n2_p407_Mazon
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spelling	todo:paper_11391138_v31_n2_p407_Mazon2023-10-03T16:08:01Z An optimal matching problem with constraints Mazón, J.M. Rossi, J.D. Toledo, J. Mass transport theory Matching problems p-Laplacian equation We deal with an optimal matching problem with constraints, that is, we want to transport two measures with the same total mass in RN to a given place (the target set), where they will match and in which we have constraints on the amount of matter we can take to points in the target set. This transport has to be done optimally, minimizing the total transport cost, that in our case is given by the sum of the Euclidean distances that each measure is transported. Here we show that such a problem has a solution. First, we solve the problem using mass transport arguments and next we perform a method to approximate the solution of the problem taking limit as p→ ∞ in a p-Laplacian type variational problem. In the particular case in which the target set is contained in a hypersurface, we deal with an optimal transport problem through a membrane, that is, we want to transport two measures which are located in different locations separated by a membrane (the hypersurface) which only let through a predetermined amount of matter. © 2018, Universidad Complutense de Madrid. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_11391138_v31_n2_p407_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 theory Matching problems p-Laplacian equation
spellingShingle	Mass transport theory Matching problems p-Laplacian equation Mazón, J.M. Rossi, J.D. Toledo, J. An optimal matching problem with constraints
topic_facet	Mass transport theory Matching problems p-Laplacian equation
description	We deal with an optimal matching problem with constraints, that is, we want to transport two measures with the same total mass in RN to a given place (the target set), where they will match and in which we have constraints on the amount of matter we can take to points in the target set. This transport has to be done optimally, minimizing the total transport cost, that in our case is given by the sum of the Euclidean distances that each measure is transported. Here we show that such a problem has a solution. First, we solve the problem using mass transport arguments and next we perform a method to approximate the solution of the problem taking limit as p→ ∞ in a p-Laplacian type variational problem. In the particular case in which the target set is contained in a hypersurface, we deal with an optimal transport problem through a membrane, that is, we want to transport two measures which are located in different locations separated by a membrane (the hypersurface) which only let through a predetermined amount of matter. © 2018, Universidad Complutense de Madrid.
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 matching problem with constraints
title_short	An optimal matching problem with constraints
title_full	An optimal matching problem with constraints
title_fullStr	An optimal matching problem with constraints
title_full_unstemmed	An optimal matching problem with constraints
title_sort	optimal matching problem with constraints
url	http://hdl.handle.net/20.500.12110/paper_11391138_v31_n2_p407_Mazon
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An optimal matching problem with constraints

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