Search results for "Monge–Kantorovich problems"
showing 2 items of 2 documents
A Monge-Kantorovich mass transport problem for a discrete distance
2011
This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obta…
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
2014
Abstract. We consider the following problem: given a bounded convex domain Ω ⊂ ℝ N ${\Omega \subset \mathbb {R}^N}$ we consider the limit as p → ∞ of solutions to - div ( b p - p | D u | p - 2 D u ) = f + - f - ${- \operatorname{div} (b_{p}^{-p} |Du|^{p-2} Du)=f_+ - f_-}$ in Ω and b p - p | D u | p - 2 ∂ u ∂ η = 0 ${ b_{p}^{-p} |Du|^{p-2} \frac{\partial u}{\partial \eta }=0}$ on ∂ Ω ${\partial \Omega }$ . Under appropriate assumptions on the coefficients bp that in particular verify that lim p → ∞ b p = b ${ \lim _{p\rightarrow \infty } b_p = b }$ uniformly in Ω ¯ ${\overline{\Omega }}$ , we prove that there is a uniform limit of u p j ${u_{p_j}}$ (along a sequence p j → ∞ ${p_j \rightarrow…