no. 4
A variational model for urban planning with traffic congestion
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 595-613.

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.

DOI : 10.1051/cocv:2005022
Classification : 49K20, 49K30
Mots clés : continuous transportation models, traffic congestion 
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     author = {Carlier, Guillaume and Santambrogio, Filippo},
     title = {A variational model for urban planning with traffic congestion},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {595--613},
     publisher = {EDP-Sciences},
     volume = {11},
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     doi = {10.1051/cocv:2005022},
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Carlier, Guillaume; Santambrogio, Filippo. A variational model for urban planning with traffic congestion. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 595-613. doi : 10.1051/cocv:2005022. http://www.numdam.org/articles/10.1051/cocv:2005022/

[1] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959) 623-727. | Zbl

[2] M. Beckmann, A continuous model of transportation. Econometrica 20 (1952) 643-660. | Zbl

[3] M. Beckmann and T. Puu, Spatial Economics: Density, Potential and Flow. North-Holland, Amsterdam (1985). | MR

[4] H. Brezis, Analyse Fonctionnelle. Masson Editeur, Paris (1983). | MR | Zbl

[5] 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. | MR | Zbl

[6] G. Buttazzo and E. Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem. Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003) 631-678. | Numdam | Zbl

[7] L. De Pascale and A. Pratelli, Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc. Var. Partial Differ. Equ. 14 (2002) 249-274. | Zbl

[8] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin (1977). | MR | Zbl

[9] R.J. Mccann, A convexity principle for interacting gases. Adv. Math. 128 (1997) 153-159. | Zbl

[10] 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).

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