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.

小行星9626382 该提案属于几何和微观局部分析的一般领域。研究人员打算继续发展退化伪微分技术，并将其应用于椭圆型偏微分方程的散射理论和谱分析。这些技术涉及退化椭圆算子的参数和广义逆的显式几何构造。 物理学和几何学中的许多问题都可以用偏微分方程组来描述。椭圆型偏微分方程--例如描述各种热流现象--在偏微分方程理论中形成了一个特别发达的分支。所提出的研究涉及椭圆型微分方程的“奇异”方面，这在理论上比光滑的情况下更困难。