Optimal Mass Transport on Metric Graphs
研究了度量图上两个等质量之间的最优运输问题，成本由图中距离决定，通过p-拉普拉斯型问题逼近找到Kantorovich势和运输密度，并给出总成本的凸优化公式。
We study an optimal mass transport problem between two equal masses on a metric graph where the cost is given by the distance in the graph. To solve this problem we find a Kantorovich potential as the limit of $p$-Laplacian--type problems in the graph where at the vertices we impose zero total flux boundary conditions. In addition, the approximation procedure allows us to find a transport density that encodes how much mass has to be transported through a given point in the graph, and also provides a simple formula of convex optimization for the total cost.