中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：赵子慧（Johns Hopkins University）
题 目：Unique continuation and the singular set of harmonic functions
时 间：2023.12.20（星期三）10:30-11:30
地 点：思源楼S813
摘 要：Unique continuation property is a fundamental property for harmonic functions, as well as a large class of elliptic and parabolic PDEs. It says that if a harmonic function vanishes at a point to infinite order, it must vanish everywhere. In the same spirit, we are interested in quantitative unique continuation problems, where we use the local growth rate of a harmonic function to deduce some global estimates, such as estimating the size of its singular or critical set. In this talk, I will talk about some recent results together with C. Kenig on boundary unique continuation.