Optimal mass transportation for costs given by Finsler distances via \(p\)-Laplacian approximations
type: Item
instance of: scholarly article
title: Optimal mass transportation for costs given by Finsler distances via \(p\)-Laplacian approximations
zbMATH Open document ID: 1385.49001
author: Noureddine Igbida
author: J. D. Rossi
author: Julian Toledo
author: J. M. Mazón
publication date: 2018-01-11T00:00:00Z
review text: In this paper, the main goal is to show that a family of variational problems of \(p\)-Laplacian type allows to get the Kantorovich potentials and transport densities of the Monge-Kantorovich mass transport problem for general Finsler costs. Moreover, this approach allows us to characterize the Euler-Lagrange equation associated to the variational Kantorovich problem. The authors also give different characterizations of the Kantorovich potentials, and a Benamou-Brenier formula of the optimal transport problem. So, they approximate a Kantorovich potential and a transport density for the mass transport problem of two measures (with the transport cost given by a Finsler distance), by taking limits, as \(p\) goes to infinity, to a family of variational problems of \(p\)-Laplacian type. They characterize the Euler-Lagrange equation associated to the variational Kantorovich problem. They also obtain different characterizations of the Kantorovich potentials and a Benamou-Brenier formula for the transport problem.
reviewed by: Hussain A. El-Saify
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6824187
zbMATH Keywords: mass transport
zbMATH Keywords: Monge-Kantorovich problems
zbMATH Keywords: Finsler metric \(p\)-Laplacian equation
zbMATH Keywords: variational problems of \(p\)-Laplacian type
zbMATH Keywords: Finsler costs
zbMATH Keywords: Kantorovich potential
MaRDI profile type: Publication
full work available at URL: acv-2015-0052
OpenAlex ID: W2474417426
cites work: Q4424462
cites work: Q4954179
cites work: Q4663947
cites work: Q4428798
cites work: The Euler Equation for Functionals with Linear Growth
cites work: Q3128806
cites work: Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
cites work: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
cites work: The Monge problem for supercritical Mañé potentials on compact manifolds
cites work: A \(p\)-Laplacian approximation for some mass optimization problems
cites work: The Monge-Kantorovich problem for distributions and applications
cites work: Energies with respect to a measure and applications to low dimensional structures
cites work: Q3379033
cites work: Q4428797
cites work: Functional analysis, Sobolev spaces and partial differential equations
cites work: Regularity properties for Monge transport density and for solutions of some shape optimization problem
cites work: Q4952326
cites work: Differential equations methods for the Monge-Kantorovich mass transfer problem
cites work: Monge's transport problem on a Riemannian manifold
cites work: The Monge problem on non-compact manifolds
cites work: Sobolev spaces on Riemannian manifolds
cites work: A Monge-Kantorovich mass transport problem for a discrete distance
cites work: An Optimal Matching Problem for the Euclidean Distance
cites work: An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
cites work: Mass transport problems for the Euclidean distance obtained as limits of \(p\)-Laplacian type problems with obstacles
cites work: Mass transport problems obtained as limits of \(p\)-Laplacian type problems with spatial dependence
cites work: Finsler interpolation inequalities
cites work: Heat flow on Finsler manifolds
cites work: Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds
cites work: Absolute continuity and summability of transport densities: simpler proofs and new estimates
cites work: Lectures on Finsler geometry
cites work: Simple proofs of some results of Reshetnyak
cites work: Q4805362
cites work: Optimal Transport
DOI: 10.1515/ACV-2015-0052
published in: Advances in the Calculus of Variations
description: scientific article; zbMATH DE number 6824187