CAREER: Spectral Theory for Singular Integrals, Validated Numerics and Elliptic Problems in Non-Lipschitz Polyhedra: Research and Outreach

职业：非利普希茨多面体中奇异积分、验证数值和椭圆问题的谱理论：研究和推广

• 批准号: 0547944
• 负责人: Irina Mitrea
• 金额: $ 40.75万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0547944&HistoricalAwards=false
• 关键词: CAREER; Spectral; Theory; Singular; Integrals

Spectral Theory for Singular Integrals, Validated Numerics and Elliptic Problems in non-Lipschitz Polyhedra: Research and Outreach.Abstract of Proposed ResearchIrena Mitrea This project is for research and education centering on the use of harmonic analysis to study elliptic partial differential equations in non-Lipschitz domains and related questions concerning singular integrals with rough kernels. A particular interest is to use validated numerics and global optimization techniques to help develop computer-aided proofs of basic results. The results of this research may have many applications in science and engineering as well as in the numerical analysis of these problems. The PI will also develop a summer program for undergraduates that provides an introduction to research in these areas and develop courses and seminars for graduate students interested in these topics.

非Lipschitz多面体中奇异积分、有效数值和椭圆问题的谱理论：研究和推广。 本项目是以利用调和分析研究非Lipschitz域上的椭圆型偏微分方程以及粗糙核奇异积分相关问题为中心的研究和教育项目。 一个特别的兴趣是使用验证的数值和全局优化技术，以帮助开发计算机辅助证明的基本结果。本研究的结果可能有许多应用在科学和工程以及在这些问题的数值分析。PI还将为本科生开发一个暑期课程，介绍这些领域的研究，并为对这些主题感兴趣的研究生开发课程和研讨会。