Harmonic Analysis and Linear Elliptic Equations

调和分析和线性椭圆方程

• 批准号: 0600389
• 负责人: Jill Pipher
• 金额: $ 17.26万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600389&HistoricalAwards=false
• 关键词: Harmonic; Analysis; Linear; Elliptic; Equations

ABSTRACTThis proposal has two parts. In part one, the set of problemsconcerns multiparameter Fourier analysis, and, in particular, a set of questions about multi-linear operators and commutators.The goal is to carry out the multi-linear theory and the Coifman-Rochberg-Weiss commutator theory to the extent possible.In part two, we consider a collection of problems concerningelliptic divergence form or non-divergence form operators withnon-smooth coefficients.The proposal concerns a set of questions and problems in thegeneral area of analysis and partial differential equations.The answers to these questions will impact scientific inquiryin any field which uses tools from "harmonic analysis" to investigate questions. Such tools have proven to be valuablein every area of the physical sciences and in many areasof the life sciences.

本建议分为两部分。第一部分是关于多参数Fourier分析的问题集，特别是关于多线性算子和算子的问题集，目的是尽可能地实现多线性理论和Coifman-Rochberg-韦斯交换子理论。我们考虑了一系列关于椭圆型散度型或非散度型算子的问题，光滑系数。该建议涉及一系列问题和问题的一般领域的分析和偏微分方程。这些问题的答案将影响科学探究在任何领域使用的工具，从“谐波分析”调查的问题。这些工具已经被证明在物理科学的每个领域和生命科学的许多领域都是有价值的。