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

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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.