Collaborative Research: L-infinity variational problems and the Aronsson equation

合作研究：L-无穷变分问题和阿伦森方程

• 批准号: 0601162
• 负责人: Changyou Wang
• 金额: --
• 依托单位: University of Kentucky Research Foundation
• 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 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0601162&HistoricalAwards=false
• 关键词: Collaborative; Research; infinity; variational; problems

L-infinity variational problems are problems where one seeks to find the maximum (or minimum) of a functional that is an expression involving the pointwise behavior of a function and its gradient. The study of such problems has become very active recently and this project will support the study of a number of important open questions in the area. A particular interest is the relationship between minimizers of the variational problems and solutions of the corresponding Aronsson equation. Other questions include the uniqueness and regularity of solutions of the Aronsson equations and the characterization of the principal eigenvalue of the infinity-Laplacian operator. These variational problems are not only interesting mathematically but arise in a number of different areas of applications. These include the determination of optimal radiation treatments in chemotherapy, in image analysis and reconstruction and in determining winning strategies in certain types of games. The results obtained under this research will help describe the mathematical models of these applications. This is a collaborative award with Dr Yifeng Yu of the University of Texas at Austin.

l-内变异问题是人们寻求找到功能的最大（或最小）的问题，该功能是涉及函数及其梯度行为的表达式。 对此类问题的研究最近变得非常活跃，该项目将支持该地区许多重要的开放问题的研究。一个特别的兴趣是各种问题的最小化和相应阿森森方程解决方案之间的关系。其他问题包括Aronsson方程解决方案解决方案的唯一性和规律性以及Infinity-Laplacian操作员主要特征值的表征。 这些变异问题不仅在数学上是有趣的，而且在许多不同的应用领域中都会出现。其中包括确定化学疗法中最佳放射治疗，图像分析和重建以及确定某些类型游戏中的获胜策略。根据这项研究获得的结果将有助于描述这些应用的数学模型。 这是德克萨斯大学奥斯汀分校的Yifeng Yu博士的合作奖。