报告内容： 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. In studying that paper, we found that their method is original and sound, but their arguments leading to the main results are skipped and difficult to follow. In the present paper, by following the main idea of Shen and Zheng (2010), we give a detailed proof for their main results. This is a joint work with Dr. Zuoquan Xu.