RETRACTED: Congested traffic dynamics, weak flows and very degenerate elliptic equations

✍ Scribed by Lorenzo Brasco; Guillaume Carlier; Filippo Santambrogio

• Book ID: 104044937
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 418 KB
• Volume: 93
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2009.06.003

✦ Synopsis

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.