Artículo
Mazón, J.M.; Rossi, J.D.; Toledo, J. "Optimal mass transport on metric graphs" (2015) SIAM Journal on Optimization. 25(3):1609-1632
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Abstract:
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of p-Laplacian-type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost. © 2015 Society for Industrial and Applied Mathematics.
Registro:
| Documento: | Artículo |
| Título: | Optimal mass transport on metric graphs |
| Autor: | Mazón, J.M.; Rossi, J.D.; Toledo, J. |
| Filiación: | Departament d'Anàlisi Matemàtica, Universitat de València, Burjassot, Valencia 46100, Spain CONICET and Depto. de Matemática, FCEyN, Universidad de Buenos Aires, Pab. I, Ciudad. Universitaria (1428), Buenos Aires, Argentina |
| Palabras clave: | Convex optimization; Metric graphs; Optimal transport; P-Laplacian; Boundary conditions; Convex optimization; Laplace transforms; Approximation procedure; Metric graphs; Optimal mass transport; Optimal transport; P-Laplacian; Total flux; Transport densities; Problem solving |
| Año: | 2015 |
| Volumen: | 25 |
| Número: | 3 |
| Página de inicio: | 1609 |
| Página de fin: | 1632 |
| DOI: | http://dx.doi.org/10.1137/140995611 |
| Título revista: | SIAM Journal on Optimization |
| Título revista abreviado: | SIAM J. Optim. |
| ISSN: | 10526234 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10526234_v25_n3_p1609_Mazon |
Referencias:
- Ambrosio, L., Lecture notes on optimal transport problems in Mathematical Aspects of Evolving Interfaces (Funchal 2000) (2003) Lecture Notes in Math. 1812, pp. 1-52. , Springer, Berlin
- Banica, V., Ignat, L.I., Dispersion for the Schrödinger equation on networks (2011) J. Math. Phys, 52, p. 083703
- Berkolaiko, G., Kuchment, P., Introduction to quantum (2013) Graphs Math. Surveys Monogr, 186. , American Mathematical Society, Providence, RI
- Bernot, M., Caselles, V., Morel, J.-M., (1955) Optimal Transportation Networks. Models and Theory Lecture Notes in Math., 2009. , Springer-Verlag, Berlin
- Buttazzo, G., Pratelli, A., Solimini, S., Stepanov, E., (1961) Optimal Urban Networks via Mass Transportation, Lecture Notes in Math., , Springer-Verlag, Berlin
- Evans, L.C., Partial differential equations (1998) Grad. Studi. Math, 19. , AMS, Providence, RI
- Evans, L.C., Gangbo, W., Differential equations methods for the Monge-Kantorovich mass transfer problem (1999) Mem. Amer. Math. Soc, 137 (653)
- Igbida, N., Mazón, J.M., Rossi, J.D., Toledo, J., A Monge-Kantorovich mass transport problem for a discrete distance (2011) J. Funct. Anal, 260, pp. 3494-3534
- Kostrykin, V., Schrader, R., Kirchhoff's rule for quantum wires (1999) J. Phys. A, 32, pp. 595-630
- Kuchment, P., Quantum graphs: I. Some basic structures (2004) Waves Random Media, 14, pp. S107-S128
- Mazón, J.M., Rossi, J.D., Toledo, J., An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary (2014) Rev. Mat. Iberoam, 30, pp. 277-308
- Mazón, J.M., Rossi, J.D., Toledo, J., An optimal matching problem for the Euclidean distance (2014) SIAM J. Math. Anal, 46, pp. 233-255
- Mazón, J.M., Rossi, J.D., Toledo, J., Mass transport problems for the Euclidean distance obtained as limits of p-Laplacian type problems with obstacles (2014) J. Differential Equations, 256, pp. 3208-3244
- Mazón, J.M., Rossi, J.D., Toledo, J., Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence (2014) Adv. Nonlinear Anal, 3, pp. 133-140
- Post, O., Spectral analysis on graph-like spaces (2012) Lecture Notes in Math., , Springer Heidelberg
- Villani, C., Topics in optimal transportation (2003) Grad. Studi. Math., 58. , AMS, Providence, RI
- Villani, C., (2009) Optimal Transport. Old and New Grundlehren Math. Wiss, 338. , Springer-Verlag, Berlin
Citas:
---------- APA ----------
Mazón, J.M., Rossi, J.D. & Toledo, J. (2015) . Optimal mass transport on metric graphs. SIAM Journal on Optimization, 25(3), 1609-1632.http://dx.doi.org/10.1137/140995611
---------- CHICAGO ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Optimal mass transport on metric graphs" . SIAM Journal on Optimization 25, no. 3 (2015) : 1609-1632.http://dx.doi.org/10.1137/140995611
---------- MLA ----------
Mazón, J.M., Rossi, J.D., Toledo, J. "Optimal mass transport on metric graphs" . SIAM Journal on Optimization, vol. 25, no. 3, 2015, pp. 1609-1632.http://dx.doi.org/10.1137/140995611
---------- VANCOUVER ----------
Mazón, J.M., Rossi, J.D., Toledo, J. Optimal mass transport on metric graphs. SIAM J. Optim. 2015;25(3):1609-1632.http://dx.doi.org/10.1137/140995611
