Mathematical Sciences: Partial Differential Equations and Several Complex Variables

数学科学：偏微分方程和几个复变量

• 批准号: 9101113
• 负责人: Nancy Stanton
• 金额: $ 3.49万
• 依托单位: University of Notre Dame
• 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: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101113&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partial; Differential; Equations

Professor Stanton will continue her research in partial differential equations related to geometry and function theory of several complex variables. In particular, she will study the singularities of kernels associated with the d"-Neumann problem including the heat kernel. She will also study the heat kernel on a CR manifold and attempt to describe the behavior of the kernel in terms of the geometry of the manifold. This award will support research in an area of mathematics which relates geometry to partial differential equations. The equations contain local information about a space and the goal of the research is to patch together this local information to obtain global geometric information. The partial differential equation which is central to this research is tied to the equation which models heat flow in a material.

斯坦顿教授将继续她的研究， 微分方程与几何和函数论 几个复杂的变量特别是，她将研究 与d”-Neumann问题有关的核的奇异性 包括热内核。她还将研究 一个CR流形，并试图描述内核的行为， 流形的几何术语。 该奖项将支持数学领域的研究 它将几何学与偏微分方程联系起来。的 方程包含关于空间和目标的局部信息 这项研究是将这些当地信息拼凑在一起， 全局几何信息偏微分方程 这是这项研究的核心， 模拟材料中的热流。