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Serrin's overdetermined problem in rough domains
张翼
(中国科学院数学与系统科学研究院)
报告时间:2024年6月12日 星期三 下午16:00-17:00
报告地点:沙河校区E404
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.
报告人简介:张翼,中国科学院数学与系统科学研究院数学所副研究员。本科毕业于best365网页,2017年在芬兰于韦斯屈莱大学获得博士学位(导师Pekka Koskela)。 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 Figalli)做博士后。2021年入职中国科学院。主要研究方向是复分析,几何测度论和偏微分方程。 文章先后发表在Duke Math. J, Comm. Pure Appl. Math.和 J. Eur. Math. Soc.等国际著名杂志上。
邀请人: 彭发