In the framework of transport theory, we are interested in the following optimization problem: given the distributions of working people and of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of from with respect to a metric which depends on the transportation network.
Mots clés : optimal networks, mass transportation problems
@article{COCV_2005__11_1_88_0,
author = {Brancolini, Alessio and Buttazzo, Giuseppe},
title = {Optimal networks for mass transportation problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {88--101},
publisher = {EDP-Sciences},
volume = {11},
number = {1},
year = {2005},
doi = {10.1051/cocv:2004032},
mrnumber = {2110615},
zbl = {1103.49002},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2004032/}
}
TY - JOUR AU - Brancolini, Alessio AU - Buttazzo, Giuseppe TI - Optimal networks for mass transportation problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 88 EP - 101 VL - 11 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004032/ DO - 10.1051/cocv:2004032 LA - en ID - COCV_2005__11_1_88_0 ER -
%0 Journal Article %A Brancolini, Alessio %A Buttazzo, Giuseppe %T Optimal networks for mass transportation problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 88-101 %V 11 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2004032/ %R 10.1051/cocv:2004032 %G en %F COCV_2005__11_1_88_0
Brancolini, Alessio; Buttazzo, Giuseppe. Optimal networks for mass transportation problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 88-101. doi : 10.1051/cocv:2004032. http://www.numdam.org/articles/10.1051/cocv:2004032/
[1] and, Selected Topics on “Analysis on Metric Spaces”. Appunti dei Corsi Tenuti da Docenti della Scuola, Scuola Normale Superiore, Pisa (2000). | Zbl
[2] and, Characterization of Optimal Shapes and Masses through Monge-Kantorovich Equation. J. Eur. Math. Soc. (JEMS) 3 (2001) 139-168. | Zbl
[3] , Problemi di Ottimizzazione in Teoria del Trasporto e Applicazioni. Master's thesis, Università di Pisa, Pisa (2002). Available at http://www.sns.it/~brancoli/
[4] , Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations. Pitman Research Notes in Mathematics Series 207. Longman Scientific & Technical, Harlow (1989). | MR | Zbl
[5] and, Optimal Shapes and Masses, and Optimal Transportation Problems, in Optimal Transportation and Applications (Martina Franca, 2001). Lecture Notes in Mathematics, CIME series 1813, Springer-Verlag, Berlin (2003) 11-52. | Zbl
[6] , and, Optimal Transportation Problems with Free Dirichlet Regions, in Variational Methods for Discontinuous Structures (Cernobbio, 2001). Progress in Nonlinear Differential Equations and their Applications 51, Birkhäuser Verlag, Basel (2002) 41-65. | Zbl
[7] and, Optimal Transportation Networks as Free Dirichlet Regions for the Monge-Kantorovich Problem. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (2003) 631-678. | Numdam | Zbl
[8] and, A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results. Arch. Rational Mech. Anal. 162 (2002) 101-135. | Zbl
[9] , The Geometry of Fractal Sets. Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (1986). | MR | Zbl
[10] , On the Transfer of Masses. Dokl. Akad. Nauk. SSSR (1942).
[11] , On a Problem of Monge. Uspekhi Mat. Nauk. (1948).
[12] , Mémoire sur la théorie des Déblais et des Remblais. Histoire de l'Acad. des Sciences de Paris (1781) 666-704.
[13] and, -convergence for the Irrigation Problem. Preprint Scuola Normale Superiore, Pisa (2003). Available at http://cvgmt.sns.it/ | MR | Zbl
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