学术报告

【online】Summer 2020 online talks on partial differential equations

发布人:发布时间: 2020-07-14

字体大小: 【小】 【中】 【大】

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: 2020723  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.

 

邀请人:陈学长老师、李军老师

 

The upcoming talks will be updated on http://maths.nju.edu.cn/~xzchen/Summer 2020.pdf .