Congested traffic dynamics , weak flows and very degenerate elliptic equations

  title={Congested traffic dynamics , weak flows and very degenerate elliptic equations},
  author={Lorenzo Brasco and Guillaume Carlier and Filippo Santambrogio},
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. 

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