Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence

Abstract

We consider the following problem: given a bounded convex domain ⊂ ℝ we consider the limit as → ∞ of solutions toUnder appropriate assumptions on the coe cients that in particular verify that lim →∞ = uniformly in , we prove that there is a uniform limit of (along a sequence → ∞) and that this limit is a Kantorovich potential for the optimal mass transport problem of + to − with cost ( , ) given by the formula ( , ) = inf (0)= , (1)= ∫ .

Optimal Mass Transport on Metric Graphs

“…in which the cost is given by the Euclidean distance or variants of it. See [8,11,12,13,14]. Here we apply these ideas to the optimal transport problem on a metric graph, showing again that this approximation procedure is quite powerful since it provides all the relevant information for the transport problem.…”