Congested traffic dynamics, weak flows and very degenerate elliptic equations
By Lorenzo Brasco, Guillaume Carlier, Filippo Santambrogio. 2010
95 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/952ed0aee36785bcba4371be13c0991e89e6a6f9
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In Applied Mathematics
- Filippo Santambrogio
- Lorenzo Brasco
- Guillaume Carlier
- Maria Colombo
- Alessio Figalli
- G. Peyr'e
- Cristiana De Filippis
- Giuseppe Mingione
In Computational Theory and Mathematics
- Filippo Santambrogio
- Lorenzo Brasco
- Guillaume Carlier
- Alessio Figalli
- Maria Colombo
- Cristiana De Filippis
- Giuseppe Mingione
- Patrick Winkert
Citations in the corpus
- Regularity results for very degenerate elliptic equations (2014, background): “[14] F.Santambrogio, V.Vespri: Continuity in two dimensions for a very degenerate elliptic equation.”
- On certain anisotropic elliptic equations arising in congested optimal transport: Local gradient bounds (2014, background): “As pointed out in [7], regularity results for minimizers of such a kind of functionals are tightly connected with optimal transport problems with congestion effects.”
- Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “On the other hand, Sobolev regularity of w and Lipschitz regularity results for u are proven in [80].”
- Geodesics for a class of distances in the space of probability measures (2012, unknown): “This result and its proof suggest a different approach to the problem, by somehow lifting the geodesics problem to a variational problem at the level of measures on curves, which is reminiscent to the work of Carlier–Jimenez–Santambrogio [5] (see also [4]).”