Optimal mass transportation for costs given by Finsler distances via \(p\)-Laplacian approximations
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.
variational problems of \(p\)-Laplacian type
scientific article; zbMATH DE number 6824187
scientific article