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.

该项目将产生有关liouville定理的基本知识，并将p最终地图定期化为p-superstronglonglonglongable的流形。 拟议的许多工作正在进行的研究中，它继续或扩展了以前的个人工作（例如，将谐波图最小化的规律性最小化至超严重的不稳定流形）和研究人员的共同工作。 它借鉴了来自几个领域的技术，包括差异几何，部分微分方程，几何测量理论，拓扑和变化的计算。 S. Walter Wei博士将研究非线性椭圆系统的几何方面和最小化器的规律性； Chi-ming Yau博士将致力于Riemannian歧管的功能理论特性。 在联合项目中，WEI和YAU将继续从外部观点开始研究平均变异方法，以此作为面对和解决全球非线性分析和几何学问题的方法。