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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 the Euclidean distance that each measure is transported. We show that such a problem has a solution with matching measure concentrated on the boundary of the target set. Furthermore we perform a method to approximate the solution of the problem taking the limit as p→∞ in a system of PDEs of p-Laplacian type. © 2014 Society for Industrial and Applied Mathematics.


Documento: Artículo
Título:An optimal matching problem for the Euclidean distance
Autor:Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament d'Anàlisi Matemàtica, Universitat de València, Valencia 46100, Spain
Departamento de Análisis Matemático, Universidad de Alicante, Alicante 03080, Spain
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Monge-Kantorovich's mass transport theory; Optimal matching problem; P-Laplacian systems; Euclidean distance; Monge-kantorovich's mass transport theories; Optimal matching; P-Laplacian; p-Laplacian systems; Transport costs; Statistical mechanics; Optimization
Página de inicio:233
Página de fin:255
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.


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---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2014) . An optimal matching problem for the Euclidean distance. SIAM Journal on Mathematical Analysis, 46(1), 233-255.
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "An optimal matching problem for the Euclidean distance" . SIAM Journal on Mathematical Analysis 46, no. 1 (2014) : 233-255.
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "An optimal matching problem for the Euclidean distance" . SIAM Journal on Mathematical Analysis, vol. 46, no. 1, 2014, pp. 233-255.
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. An optimal matching problem for the Euclidean distance. SIAM J. Math. Anal. 2014;46(1):233-255.