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

奇异积分的谱理论，非Lipschitz多面体中的验证数值和椭圆问题：研究和展望。建议的研究摘要Irena Mitrea这个项目是研究和教育的，主要是使用调和分析来研究非Lipschitz区域上的椭圆型偏微分方程组以及与带有粗糙核的奇异积分有关的问题。特别感兴趣的是使用经过验证的数值和全局优化技术来帮助开发基本结果的计算机辅助证明。这一研究成果在科学和工程以及这些问题的数值分析中可能会有很多应用。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。

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.