报告题目： Overview on the mass transportation problem　　

　　报告人：汪徐家 院士（Australian National University）

　　报告时间： 2018年1月16日 10：00 --12：00　　

　　报告地点： 武汉物数所新波谱楼1217会议室　　

　　专家简介：汪徐家院士（ Fellowship of the Australian Academy of Science，elected in 2009 ），世界著名数学家，非线性偏微分方程权威。1963年9月出生于浙江省淳安县（现千岛湖），1979年9月到1983年7月就读于浙江大学数学系本科。1983年9月到1990年7月,浙江大学数学系硕士生、博士生，师从董光昌教授，研究方向为偏微分方程。1990年8月到1995年8月，浙江大学数学系任教。1995年9月至今，在澳大利亚国立大学从事数学研究。2003年到2007年，为南开大学数学系长江讲座教授。2002年至今，为浙江大学客座教授。2002年获澳大利亚数学会奖章(Australian Mathematical Society Medal,2002). Invited speaker, 2002 International Congress of Mathematicians。2007年获第四届华人数学家大会晨兴数学金奖。　　

　　Abstract: The optimal transportation problem was first introduced by Monge in 1781. By Kantorovich's duality, this problem can be formulated as a Monge-Ampere type equation subject to the second boundary condition. For the special quadratic cost function, the existence and regularity have been settled down two decades ago. For general cost functions, the existence and regularity of solutions have been obtained under certain conditions. But the natural cost function, namely when the cost is proportional to the distance the mass is transported, is at the borderline of these conditions. With my collaborators Qi-Rui Li and Filippo Santambrogio, we recently studied the regularity of Monge's problem and discovered some delicate results. We proved that in a smooth approximation, the eigenvalues of the Jacobian matrix of the optimal mapping are uniformly bounded but the mapping itself may not be Holder continuous. But in dimension two the mapping is continuous. In this talk I will discuss recent developments in this direction.