Calculus of Variations

Abstract

Monge’s problem refers to the classical problem of optimally transporting mass: given Borel probability measures μ = μ− on R, find the measure preserving map s(x) between them which minimizes the average distance transported. Here distance can be induced by the Euclidean norm, or any other uniformly convex and smooth norm d(x, y) = ‖x− y‖ onR. Although the… (More)

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