报告题目：Serrin's overdetermined problem in rough domains

报 告 人：张翼副研究员（中科院数学与系统科学研究院）

报告时间：2024年7月30日  9:00-10:00

报告地点：理学院五楼数学研究中心报告厅（528）

报告摘要：

The classical Serrin's overdetermined theorem states that a $C^2$ bounded domain, which admits a function with constant Laplacian that satisfies both constant Dirichlet and Neumann boundary conditions, must necessarily be a ball. While extensions of this theorem to non-smooth domains have been explored since the 1990s, the applicability of Serrin's theorem to Lipschitz domains remained unresolved. In this talk we discuss about this problem, showing that the result holds for domains that are sets of finite perimeter with a uniform upper bound on the density, and it also allows for slit discontinuities. This is based on a recent joint work with Figalli.

报告人简介：

张翼，中科院数学与系统科学学院副研究员，国家青年人才项目获得者。博士毕业于芬兰于韦斯屈莱大学（University of Jyvaskyyla），导师为Pekka Koskela教授。先后在德国豪斯多夫数学研究所（导师Herbert Koch），瑞士苏黎世联邦理工学院（导师Alessio Figali）做博士后。2021年入职中国科学院。主要研究方向为复分析、几何测度论和偏微分方程等，已在《Duke Math. J.》《J. Eur. Math.Soc.》《Comm. Pure App. Math.》《J. Math. Pures Appl.》《Arch. Ration. Mech. Anal.》等权威数学杂志发表学术论文二十余篇。