Congested traffic dynamics, weak flows and very degenerate elliptic equations |
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| Authors: | Lorenzo Brasco Guillaume Carlier Filippo Santambrogio |
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| Institution: | 1. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, 56127 Pisa, Italy;2. CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France;3. DMA, École Normale Supérieure de Paris, 45, rue d''Ulm, 75230 Paris Cedex 05, France |
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| Abstract: | 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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