Calculus of Variations and Geometric Measure Theory

L. Brasco - G. Carlier - F. Santambrogio

Congested traffic dynamics, weak flows and very degenerate elliptic equations

created by santambro on 19 Mar 2009
modified by brasco on 08 Oct 2013


Accepted Paper

Inserted: 19 mar 2009
Last Updated: 8 oct 2013

Journal: J. Math. Pures Appl.
Year: 2010


Starting from a model of traffic congestion, we introduce a minimal-flow--like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in some cases to apply the DiPerna-Lions theory

Keywords: Traffic congestion, regularity, Di Perna - Lions, Degenerate elliptic PDEs