A decomposition theorem of surface vector fields and spectral structure of the Neumann-Poincare operator in elasticity
科研大讨论系列报告
报告题目(Title)：A decomposition theorem of surface vector fields and spectral structure of the Neumann-Poincare operator in elasticity
报告人(Speaker)：Professor Hyeonbae Kang (Inha University,Korea)
地点(Place)：后主楼 1223
时间(Time)： 2025年 1 月 15 日（周三）15:00-16:00
邀请人(Inviter)：Haigang Li,Yanyan Li
报告摘要
We show that vector fields on the boundary of a bounded domain in three dimensions is decomposed into three parts: the first one extends to the inside the domain as a divergence-free and rotation-free vector field, the second one to the outside as a divergence-free and rotation-free vector field, and the third one to both the inside and the outside as divergence-free harmonic vector fields. We apply this decomposition theorem to investigate spectral properties of the Neumann-Poincar\'e operator in elasticity, whose cubic polynomial is known to be compact. We show that each linear factor of the cubic polynomial is compact on each subspace of decomposition separately and those subspaces characterize eigenspaces of the Neumann-Poincar\'e operator. This talk is based on joint works with S. Fukushima and Y.-G. Ji.
主讲人简介
Hyeonbae Kang，2022年国际数学大会邀请报告人，韩国工业与应用数学会（Korean Society for Industrial and Applied Mathematics）理事长，韩国科学技术院院士，仁荷大学数学系Jungseok讲座教授，2014年国际数学家大会（2014 International Congress of Mathematicians）组委（执委）成员和竞选委员会成员。Kang教授本科和硕士分别于1982年和1984年毕业于首尔国立大学，1989年获得美国威斯康星大学-麦迪逊分校的数学博士学位。曾担任首尔国立大学教授、通识教育院副院长，韩国数学会秘书长，2008年加入韩国仁荷大学数学系任Jungseok讲座教授，2011年至今担任应用数学所所长，曾获韩国科学奖（总统奖）、韩国最佳研究论文奖，最佳学术成就奖等荣誉。Kang教授的主要研究领域包括复合材料中的偏微分方程理论，反问题及数学成像，谱分析，渐进分析等，在复合材料中的Babuska问题、Neumann-Poincar\'e算子等方面做出了许多重要的工作。
