Congested traffic equilibria and degenerate anisotropic PDEs

Carlier, Guillaume; Brasco, Lorenzo

Carlier, Guillaume; Brasco, Lorenzo (2013), Congested traffic equilibria and degenerate anisotropic PDEs, Dynamic Games and Applications, 3, 4, p. 508-522. http://dx.doi.org/10.1007/s13235-013-0081-z

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00734555

Date

2013

Journal name

Dynamic Games and Applications

Volume

Number

Publisher

Springer

Pages

508-522

Abstract (EN)

Congested traffic problems on very dense networks lead, at the limit, to minimization problems posed on measures on curves as shown in Baillon and Carlier (Netw. Heterogenous Media 7: 219--241, 2012). Here, we go one step further by showing that these problems can be reformulated in terms of the minimization of an integral functional over a set of vector fields with prescribed divergence. We prove a Sobolev regularity result for their minimizers despite the fact that the Euler-Lagrange equation of the dual is highly degenerate and anisotropic. This somehow extends the analysis of Brasco et al. (J. Math. Pures Appl. 93: 652--671, 2010) to the anisotropic case.

Subjects / Keywords

regularity; anisotropic and degenerate PDEs; traffic congestion