Harmonic Analysis and Partial Differential Equations

调和分析和偏微分方程

• 批准号: 0456583
• 负责人: Carlos Kenig
• 金额: --
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0456583&HistoricalAwards=false
• 关键词: Harmonic; Analysis; Partial; Differential; Equations

Harmonic Analysis and Partial Differential EquationsProject AbstractCarlos E. KenigThe proposal will be a continuation of the PI's research on the regularity of solutions to free boundary problems, the analysis of boundary value problems under minimal smoothness conditions, the development of Liouville type theorems for viscous conservation laws, the development of techniques from Fourier analysis to study qualitative and quantitative properties of solutions of nonlinear dispersive equations and the use of quantitative unique continuation methods to study Anderson localization and the inverse problem in electrical impedance tomography. These partial differential equations arise in quantum mechanical models, fluid mechanics and tomography theory amongst other areas so the analysis of these equations may have many applications.

调和分析和偏微分方程项目摘要卡洛斯·E·肯格这项提议将是PI关于自由边界问题解的正则性、最小光滑条件下的边值问题的分析、粘性守恒定律的Liouville类型定理的发展、从傅立叶分析到研究非线性色散方程解的定性和定量性质的技术的发展以及使用定量的唯一延拓方法来研究电阻抗层析成像中的Anderson局部化和反问题。这些偏微分方程出现在量子力学模型、流体力学和层析成像理论等领域，因此对这些方程的分析可能会有很多应用。