Fully Nonlinear Equations

完全非线性方程

• 批准号: 0500808
• 负责人: Yu Yuan
• 金额: --
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500808&HistoricalAwards=false
• 关键词: Fully; Nonlinear; Equations

Fully Nonlinear EquationsProject AbstractYu YuanThis project focuses on the regularity and solvability of fully nonlinear equations. The first topic is to investigate Bernstein/Liouville problems for various equations. Here the aim is to prove that the only solutions of certain problems are certain very simple or "trivial" solutions. Another topic is to prove regularity results for the solutions of fully nonlinear second order elliptic equations in 3d domains and also for the Isaacs' equation of control theory. The project will also look at deriving necessary conditions for the local isometric imbedding problem for 2-dimensional Riemannian manifolds. The partial differential equations in the project arise not only in geometry but also in science and engineering. Results on these problems should have applications to stringtheory in modern physics, for nonlinear elasticity in mechanics, and for stochastic optimal control theory in engineering and economics.

完全非线性方程式摘要Yuanthis项目着重于完全非线性方程的规律性和可溶性。第一个主题是调查伯恩斯坦/liouville的各种方程式问题。这里的目的是证明某些问题的唯一解决方案是某些非常简单或“微不足道”的解决方案。另一个主题是证明3D域中完全非线性二阶椭圆方程以及ISAACS的控制理论方程的解决方案的解决方案。该项目还将考虑为二维Riemannian歧管的局部等距嵌入问题提供必要条件。该项目中的部分微分方程不仅在几何形状上，而且在科学和工程上都出现。 这些问题的结果应在现代物理学，机械师的非线性弹性以及工程和经济学中的随机最佳控制理论中应用弦理论。