A continuous theory of traffic congestion and Wardrop equilibria

DOI10.1007/s10958-012-0715-5zbMath1262.90016OpenAlexW2066534571MaRDI QIDQ1762538

Guillaume Carlier, Filippo Santambrogio

Publication date: 27 November 2012

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://basepub.dauphine.fr/handle/123456789/8359

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Transportation, logistics and supply chain management (90B06)

Related Items (8)

Optimal control of the mean field equilibrium for a pedestrian tourists' flow model ⋮ A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks ⋮ Higher regularity for minimizers of very degenerate convex integrals ⋮ Higher regularity in congested traffic dynamics ⋮ Lecture notes on variational mean field games ⋮ Sharp semi-concavity in a non-autonomous control problem and \(L^p\) estimates in an optimal-exit MFG ⋮ Minimal-time mean field games ⋮ Higher regularity for minimizers of very degenerate integral functionals

Cites Work

• Continuity in two dimensions for a very degenerate elliptic equation
• Derivatives with respect to metrics and applications: subgradient marching algorithm
• Ordinary differential equations, transport theory and Sobolev spaces
• On a partial differential equation involving the Jacobian determinant
• Optimal transportation networks. Models and theory
• Mean field games
• Absolute continuity and summability of transport densities: simpler proofs and new estimates
• Regularity properties for Monge transport density and for solutions of some shape optimization problem
• From discrete to continuous Wardrop equilibria
• Numerical approximation of continuous traffic congestion equilibria
• Markovian traffic equilibrium
• The Least Action Principle and the Related Concept of Generalized Flows for Incompressible Perfect Fluids
• Optimal Transportation with Traffic Congestion and Wardrop Equilibria
• A Viscosity Solutions Approach to Shape-From-Shading
• On the Volume Elements on a Manifold
• A Continuous Model of Transportation
• Congested traffic dynamics, weak flows and very degenerate elliptic equations
• Optimal Transport
• Unnamed Item
• Unnamed Item

This page was built for publication: A continuous theory of traffic congestion and Wardrop equilibria