Artículo
Mazón, J.M.; Rossi, J.D.; Toledo, J. "On optimal matching measures for matching problems related to the euclidean distance" (2014) Mathematica Bohemica. 139(4):553-566
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | On optimal matching measures for matching problems related to the euclidean distance |
| Autor: | Mazón, J.M.; Rossi, J.D.; Toledo, J. |
| Filiación: | Departament d’Anàlisi Matemàtica, Universitat de València, Avda. Doctor Moliner 50, Burjassot, València, 46100, Spain Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, Alicante, 03080, Spain Depto. De Matemática, FCEyN UBA, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina |
| Palabras clave: | Mass transport; Monge-Kantorovich problem; P-Laplacian equation |
| Año: | 2014 |
| Volumen: | 139 |
| Número: | 4 |
| Página de inicio: | 553 |
| Página de fin: | 566 |
| Título revista: | Mathematica Bohemica |
| Título revista abreviado: | Math. Bohem. |
| ISSN: | 08627959 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08627959_v139_n4_p553_Mazon |
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Citas:
---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2014) . On optimal matching measures for matching problems related to the euclidean distance. Mathematica Bohemica, 139(4), 553-566.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08627959_v139_n4_p553_Mazon [ ]
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "On optimal matching measures for matching problems related to the euclidean distance" . Mathematica Bohemica 139, no. 4 (2014) : 553-566.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08627959_v139_n4_p553_Mazon [ ]
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "On optimal matching measures for matching problems related to the euclidean distance" . Mathematica Bohemica, vol. 139, no. 4, 2014, pp. 553-566.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08627959_v139_n4_p553_Mazon [ ]
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. On optimal matching measures for matching problems related to the euclidean distance. Math. Bohem. 2014;139(4):553-566.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08627959_v139_n4_p553_Mazon [ ]
