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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Roméo Hatchi

10 Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations

Roméo Hatchi, CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France, hatchi@ceremade.dauphine.fr

Abstract: As shown in [16], under some structural assumptions, working on congested traffic problems in general and increasingly dense networks leads, at the limit by Γ-convergence, to continuous minimization problems posed on measures on generalized curves. Here we show the equivalence with another problem that is the variational formulation of an anisotropic, degenerate and elliptic PDE. For particular cases, we prove a Sobolev regularity result for the minimizers of the minimization problem ...

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