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A variational model for urban planning withtraffic congestion

Published online by Cambridge University Press:  15 September 2005

Guillaume Carlier  and
Filippo Santambrogio
Guillaume Carlier
Affiliation:
Université Paris Dauphine, CEREMADE, UMR CNRS 7534, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France; carlier@ceremade.dauphine.fr
Filippo Santambrogio
Affiliation:
Scuola Normale Superiore, Classe di Scienze, Piazza dei Cavalieri 7, 56126, Pisa, Italy; f.santambrogio@sns.it
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Abstract

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

Keywords

Continuous transportation modelstraffic congestion.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 4 , October 2005 , pp. 595 - 613
Copyright
© EDP Sciences, SMAI, 2005

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References

Agmon, S., Douglis, A. and Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959) 623–727. CrossRef
Beckmann, M., A continuous model of transportation. Econometrica 20 (1952) 643–660. CrossRef
M. Beckmann and T. Puu, Spatial Economics: Density, Potential and Flow. North-Holland, Amsterdam (1985).
H. Brezis, Analyse Fonctionnelle. Masson Editeur, Paris (1983).
G. Buttazzo and F. Santambrogio, A model for the optimal planning of an urban area. Preprint available at cvgmt.sns.it (2003). To appear in SIAM J. Math. Anal.
Buttazzo, G. and Stepanov, E., Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem. Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003) 631–678.
De Pascale, L. and Pratelli, A., Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc. Var. Partial Differ. Equ. 14 (2002) 249–274. CrossRef
D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin (1977).
McCann, R.J., A convexity principle for interacting gases. Adv. Math. 128 (1997) 153–159. CrossRef
F. Santambrogio, Misure ottime per costi di trasporto e funzionali locali (in italian), Laurea Thesis, Università di Pisa, advisor: G. Buttazzo, available at www.unipi.it/etd and cvgmt.sns.it (2003).