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Mathematics > Optimization and Control

arXiv:1409.3337 (math)
[Submitted on 11 Sep 2014]

Title:A Note on the Monge-Kantorovich Problem in the Plane

Authors:Zuo Quan Xu, Jia-An Yan
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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.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1409.3337 [math.OC]
  (or arXiv:1409.3337v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1409.3337
Journal reference: Communications on Pure and Applied Analysis, Vol.14 (2015), 517-525
Related DOI: https://doi.org/10.3934/cpaa.2015.14.517

Submission history

From: Zuo Quan Xu Dr. [view email]
[v1] Thu, 11 Sep 2014 07:02:09 UTC (7 KB)
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