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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2018
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11391138_v31_n2_p407_Mazon http://hdl.handle.net/20.500.12110/paper_11391138_v31_n2_p407_Mazon |
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paper:paper_11391138_v31_n2_p407_Mazon2023-06-08T16:09:14Z An optimal matching problem with constraints 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. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11391138_v31_n2_p407_Mazon 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 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. |
| 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 |
| publishDate |
2018 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_11391138_v31_n2_p407_Mazon http://hdl.handle.net/20.500.12110/paper_11391138_v31_n2_p407_Mazon |
| _version_ |
1768546687474728960 |