Calculus of Variations and Geometric Measure Theory

G. Buttazzo - F. Santambrogio

A Model for the Optimal Planning of an Urban Area

created on 07 Dec 2003
modified by santambro on 02 Nov 2005


Published Paper

Inserted: 7 dec 2003
Last Updated: 2 nov 2005

Journal: SIAM J. Math. Anal.
Volume: 37
Number: 2
Pages: 514-530
Year: 2005


We propose a model to describe the optimal distributions of residents and services in a prescribed urban area. The cost functional takes into accounts the transportation costs (according to a Monge-Kantorovich type criterion) and two additional terms which penalize concentration of residents and dispersion of services. The tools we use are the Monge-Kantorovich mass transportation theory and the theory of nonconvex functionals defined on measures.

Keywords: urban planning, Mass transportation, Nonconvex Functionals over Measures