最优运输问题和非线性偏微分方程

This advanced seminar project mainly focuses on three important scientific problems in the field of optimal mass transportation problem and related nonlinear partial differential equations:1)optimal transportation problems on manifolds with complex topological structures and unbalance optimal transportation problems; 2)regularity of degenerate Monge-Ampere type equations; 3) applications of optimal transportation theory in fluid mechanics and image processing. We are planning to invite the Chinese young scholars to carry out a series of specific topic seminars, discussions and collaborations to concentrate on the problems. It is expected to cultivate a Chinese research group and promote the ability and level of the Chinese research group in this direction.

该高级研讨班项目主要聚焦最优运输问题和非线性偏微分方程方向的三个重要科学问题：1）具有复杂拓扑结构流形上的最优质量运输问题和非平衡的最优质量运输问题；2）退化的Monge-Ampere型方程解的正则性；3）最优质量运输理论在流体力学和图像处理上的应用，组织国内有关中青年学者开展专题研讨、交流和合作，集中探索和攻关，努力提升在该研究方向的能力和水平，形成研究队伍。