On Fluid mechanics formulation of Monge-Kantorovich Mass Transfer Problem
نویسنده
چکیده
The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control prblem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.
منابع مشابه
Remarks on Γ-Convergence and the Monge-Kantorovich Mass Transfer Problem
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