OPTIMIZATION PROBLEMS IN MASS TRANSPORTATION THEORY ...

As an application of the theorem above weconsider the diffusion case when Ω = R N .The concentration case in the unboundedsetting still presents some extra difficultiesthat we did not yet solve. We take:• d the Wasserstein distance;• d ′ the distance metrizing the weak* topologyon probabilities:d ′ (µ, ν) =∞∑k=12 −k1 + c k∣ ∣〈φk , µ − ν〉 ∣ ∣where (φ k ) is a dense sequence of Lipschitzfunctions in the unit ball of C b (Ω)and c k are their Lipschitz constants.We may prove that the assumptions of theabstract scheme are fulfilled, and we have(for the diffusion case):62