Mathematical Sciences: Liouville Theorems and Regularity of Mappings Minimizing the Lp Norm of the Gradient

数学科学：刘维尔定理和最小化梯度 Lp 范数的映射正则性

• 批准号: 8802745
• 负责人: Shihshu Walter Wei
• 金额: $ 4.1万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-15 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802745&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Liouville; Theorems; Regularity

This project will yield basic knowledge of Liouville theorems and regularity of p-minimizing maps into p-superstrongly unstable manifolds. Much of the proposed work is ongoing research that continues or extends previous individual work (e.g. regularity of minimizing harmonic maps in to super-strongly unstable manifolds) and joint work of the investigators. It draws on techniques from several areas, including differential geometry, partial differential equations, geometric measure theory, topology and calculus of variations. Dr. S. Walter Wei will work on geometric aspects of nonlinear elliptic systems and the regularity of minimizers; Dr. Chi-Ming Yau will work on Function theoretic properties of Riemannian manifolds. In joint projects, Wei and Yau will continue to study the average variational method from an extrinsic view point as an approach to confront and resolve problems in global nonlinear analysis and geometry.

该项目将产生刘维尔定理的基本知识以及将 p 极小化映射到 p 超强不稳定流形的规律性。 拟议的大部分工作是正在进行的研究，继续或扩展以前的个人工作（例如，最小化谐波映射到超强不稳定流形的规律）和研究人员的联合工作。 它借鉴了多个领域的技术，包括微分几何、偏微分方程、几何测度论、拓扑和变分法。 S. Walter Wei 博士将研究非线性椭圆系统的几何方面和极小值的正则性； Chi-Ming Yau 博士将研究黎曼流形的函数理论性质。 在联合项目中，魏和丘将继续从外在的角度研究平均变分法，作为面对和解决全局非线性分析和几何问题的方法。