The ∞-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps
نویسندگان
چکیده
We consider the nonlinear optimal transportation problem of minimizing the cost functional C∞(λ) = λess sup(x,y)∈Ω2 |y−x| in the set of probability measures on Ω having prescribed marginals. This corresponds to the question of characterizing the measures that realize the in nite Wasserstein distance. We establish the existence of local solutions and characterize this class with the aid of an adequate version of cyclical monotonicity. Moreover, under natural assumptions, we show that local solutions are induced by transport maps.
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عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 40 شماره
صفحات -
تاریخ انتشار 2008