【online】Summer 2020 online talks on partial differential equations
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Summer 2020 online talks on partial differential equations
题目: The Loewner-Nirenberg Problem in Cones
报告人：韩青 (University of Notre Dame)
时间： 2020年7月23日 9:00-10:00
报告方式：Zoom会议室 ID: 654 3755 6390 PW: 20200430
摘要: Loewner and Nirenberg discussed complete metrics conformal to the Euclidean metric and with a constant scalar curvature in bounded domains in the Euclidean space. The conformal factors blow up on boundary. The asymptotic behaviors of the conformal factors near boundary are known in $C^2$-domains. In this talk, we discuss asymptotic behaviors near vertices of cones. We will prove that solutions on finite cones are well-approximated by the solution in the corresponding infinite cone. To derive optimal estimates, we need to study a class of elliptic operators over spherical domains. These operators are singular on boundary. We will study the eigenvalue problem with the homogeneous Dirichlet boundary value and investigate boundary behaviors of the eigenfunctions.
The upcoming talks will be updated on http://maths.nju.edu.cn/~xzchen/Summer 2020.pdf .