Geometry on the Set of Probability Measures

概率测度集的几何

• 批准号: 0600791
• 负责人: Wilfrid Gangbo
• 金额: $ 20.4万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600791&HistoricalAwards=false
• 关键词: Geometry; Set; Probability; Measures

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.

关于概率测度集的几何。拟研究摘要甘波（wilfrid Gangbo）本课题旨在分析与偏微分方程相关的某些变分问题及其应用。一个主要的主题是Monge-Kantorovich大众运输问题及其应用。在一定概率测度空间上的无限维哈密顿系统的理论，包括vlasov型方程和半地转方程等例子。另一类问题是弹性理论中出现的非线性抛物方程系统，以及在某些意义上最优的框架和结构的设计。在这个项目中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。目标始终是确定过程发生的最佳方式；因此，研究结果具有重要意义和广泛的适用性。