Harmonic Analysis and Partial Differential Operators

谐波分析和偏微分算子

• 批准号: DP140100649
• 负责人: Prof Xuan Thinh Duong
• 金额: $ 25.54万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100649
• 关键词: Harmonic; Analysis; Partial; Differential; Operators

Harmonic Analysis has played an important role in the study of partial differential equations, operator theory, function spaces with wide applications. This project aims to study partial differential equations with non-smooth coefficients on domains with rough boundaries and on general metric spaces. The proposed problems are at the frontier of harmonic analysis and spectral analysis. Expected outcomes are solutions to a number of key long-standing open problems in harmonic analysis, new original ideas and new techniques with wide scopes of applications in mathematical research.

调和分析在偏微分方程组、算子理论、函数空间的研究中起着重要的作用，有着广泛的应用。本项目旨在研究具有粗糙边界的区域上和一般度量空间上的具有非光滑系数的偏微分方程。所提出的问题处于调和分析和频谱分析的前沿。预期的结果是解决调和分析中一些长期悬而未决的关键问题，新的原创想法和在数学研究中具有广泛应用范围的新技术。