A Note on the Monge-Kantorovich Problem in the Plane
Optimization and Control
2022-01-07 v1
Abstract
The Monge-Kantorovich mass-transportation problem has been shown to be fundamental for various basic problems in analysis and geometry in recent years. Shen and Zheng (2010) proposed a probability method to transform the celebrated Monge-Kantorovich problem in a bounded region of the Euclidean plane into a Dirichlet boundary problem associated to a nonlinear elliptic equation. Their results are original and sound, however, their arguments leading to the main results are skipped and difficult to follow. In the present paper, we adopt a different approach and give a short and easy-followed detailed proof for their main results.
Keywords
Cite
@article{arxiv.1409.3337,
title = {A Note on the Monge-Kantorovich Problem in the Plane},
author = {Zuo Quan Xu and Jia-An Yan},
journal= {arXiv preprint arXiv:1409.3337},
year = {2022}
}