Mathematical Sciences: Methods for Solutions of Some Nonlinear Eliptic Equations

数学科学：一些非线性椭圆方程的解法

• 批准号: 9116949
• 负责人: Wenxiong Chen
• 金额: --
• 依托单位: Missouri State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1993-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9116949&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Methods; Solutions; Some

Professor Chen will work on the problem of prescribing curvature on manifolds which have the topological type of a sphere. In addition, he will attempt to apply variational methods to reprove the classical uniformization theorem and prove an extension of the theorem to surfaces with conical singularities. Variational methods will also be used to classify solutions of some nonlinear partial differential equations of differential geometry and to study solutions of nonlinear elliptic boundary value problems for domains in Euclidean space. The research supported by this award is frequently referred to as global analysis. It attempts to find and describe global solutions to nonlinear partial differential equations on a surface or manifold. These equations describe local properties of the surface such as curvature. The research, therefore, seeks to relate local information to global information.

陈教授将研究具有球面拓扑型的流形上的曲率规定问题。此外，他还将尝试应用变分方法重新证明经典的均匀化定理，并证明该定理在具有圆锥奇点的曲面上的推广。我们还将用变分方法对一些非线性微分几何偏微分方程解进行分类，并研究欧氏空间中区域的非线性椭圆型边值问题的解。该奖项支持的研究经常被称为全球分析。它试图寻找和描述曲面或流形上的非线性偏微分方程解的整体。这些方程描述了曲面的局部属性，如曲率。因此，这项研究试图将本地信息与全球信息联系起来。