The $\infty$-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps

We consider the non-nonlinear optimal transportation problem of minimizing the cost functional $\mathcal{C}_\infty(\lambda) = \operatornamewithlimits{\lambda-ess\,sup}_{(x,y) \in \Omega^2} |y-x|$ in the set of probability measures on $\Omega^2$ having prescribed marginals. This corresponds to the qu... View More