Geometry on the Set of Probability Measures

概率测度集上的几何.研究建议摘要 这个项目是分析与偏微分方程有关的某些变分问题及其应用。一个主要的主题是Monge-Kantorovich质量运输问题及其应用。也理论的无穷维哈密顿系统的某些空间的概率措施，包括例子，如弗拉索夫型方程和半地转方程。 另一类问题是弹性理论中出现的非线性抛物方程组，以及在某种意义上是最优的框架和结构的设计。这个项目所要研究的问题在许多不同的领域都有应用，包括经济学、物理学、地球科学和工程学。目标总是确定过程发生的最佳方式;因此结果可能非常重要并具有广泛的适用性。

Geometry on the Set of Probability Measures.Abstract of Proposed ResearchWilfrid Gangbo This project is to analyze certain variational problems connected with partial differential equations and applications. A primary topic is the Monge-Kantorovich mass transportation problem and its applications. Also the theory of infinite dimensional Hamiltonian systems on certain spaces of probability measures including examples such as Vlasov-type equations and the semi-geostrophic equation. Another class of problems are the systems of nonlinear parabolic equations that arise in elasticity theory and the design of frames and structures which are optimal in certain senses. The problems to be studied in this project have applications in many different areas including economics, physics, geosciences and engineering. The aim is always to identify the optimal way for a process to occur; so the results may be very important and have wide applicability.