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Abstract:

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.

Registro:

Documento: Artículo
Título:An optimal matching problem with constraints
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d’Anàlisi Matemàtica, Universidad de València, Valencia, Spain
Departamento de Matemáticas, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Mass transport theory; Matching problems; p-Laplacian equation
Año:2018
Volumen:31
Número:2
Página de inicio:407
Página de fin:447
DOI: http://dx.doi.org/10.1007/s13163-018-0256-7
Título revista:Revista Matematica Complutense
Título revista abreviado:Rev. Mat. Complutense
ISSN:11391138
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11391138_v31_n2_p407_Mazon

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Citas:

---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2018) . An optimal matching problem with constraints. Revista Matematica Complutense, 31(2), 407-447.
http://dx.doi.org/10.1007/s13163-018-0256-7
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "An optimal matching problem with constraints" . Revista Matematica Complutense 31, no. 2 (2018) : 407-447.
http://dx.doi.org/10.1007/s13163-018-0256-7
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "An optimal matching problem with constraints" . Revista Matematica Complutense, vol. 31, no. 2, 2018, pp. 407-447.
http://dx.doi.org/10.1007/s13163-018-0256-7
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. An optimal matching problem with constraints. Rev. Mat. Complutense. 2018;31(2):407-447.
http://dx.doi.org/10.1007/s13163-018-0256-7