On Monge-Kantorovich Problem in the Plane
Probability
2008-03-20 v1 Analysis of PDEs
Abstract
We transfer the celebrating Monge-Kontorovich problem in a bounded domain of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with order term missing in its diffusion coefficients: \begin{eqnarray*} A(x, F'_x)F''_{xx}+B(y, F'_y)F''_{yy}&=&C(x, y, F'_x, F'_y) \end{eqnarray*} where and are functions based on the initial distributions, is an unknown probability distribution function and therefore closed the former problem.
Cite
@article{arxiv.0803.2830,
title = {On Monge-Kantorovich Problem in the Plane},
author = {Yinfang Shen and Weian Zheng},
journal= {arXiv preprint arXiv:0803.2830},
year = {2008}
}