Mathematical Sciences: Degenerate Microlocal Methods in Geometric Analysis

数学科学：几何分析中的简并微局域方法

• 批准号: 9626382
• 负责人: Rafe Mazzeo
• 金额: $ 6万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626382&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Degenerate; Microlocal; Methods

9626382 Mazzeo This proposal is in the general area of geometric and microlocal analysis. The investigator intends to continue the development of degenerate pseudodifferential techniques and to apply them to scattering theory and spectral analysis of elliptic partial differential equations. These techniques involve explicit geometric constructions of parametrics and generalized inverses for degenerate elliptic operators. Many problems in physics and geometry can be described by systems of partial differential equations. Elliptic partial differential equations - describing, for example, various heat flow phenomena - form a particularly well-developed branch within the theory of partial differential equations. The proposed research deals with the 'singular' aspect of elliptic differential equations which are theoretically more difficult than the smooth case.

9626382 Mazzeo该建议在几何和微局部分析的一般领域。研究人员打算继续发展堕胎假数技术，并将其应用于椭圆形偏微分方程的散射理论和光谱分析。这些技术涉及对参数的明确几何结构和简并椭圆运算符的广义逆。 物理和几何形状的许多问题可以通过部分微分方程的系统来描述。椭圆形偏微分方程（例如，描述各种热流现象）在部分微分方程理论中形成了一个特别发达的分支。拟议的研究涉及椭圆差方程的“奇异”方面，这些方程在理论上比平滑案例更加困难。