A mixed formulation of the Monge-Kantorovich equations

John W. Barrett, Leonid Prigozhin

    Research output: Contribution to journalArticlepeer-review

    19 Scopus citations


    We introduce and analyse a mixed formulation of the Monge-Kantorovich equations, which express optimality conditions for the mass transportation problem with cost proportional to distance. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments, where both the optimal transport density and the associated Kantorovich potential are computed for a coupling problem and problems involving obstacles and regions of cheap transportation.

    Original languageEnglish
    Pages (from-to)1041-1060
    Number of pages20
    JournalESAIM: Mathematical Modelling and Numerical Analysis
    Issue number6
    StatePublished - 1 Nov 2007


    • Convergence analysis
    • Existence
    • Finite elements
    • Mixed methods
    • Monge-Kantorovich problem
    • Optimal transportation

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Modeling and Simulation
    • Computational Mathematics
    • Applied Mathematics


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