报告题目:Spectral properties of the Neumann-Poincaré on rotationally symmetric domains

报告人：Yong-Gwan Ji 博士后研究员 (韩国高等科学院)

报告时间：2024年4月22日 14:30-15:30

报告地点：理学楼A110

摘要：We concern the spectral properties of the Neumann-Poincaré (NP) operator on two- and three-dimensional bounded domains which are invariant under either rotation or reflection. We prove that if the domain has such a symmetry, then the function space on which the NP operator acting is decomposed into invariant subspaces defined as eigenspaces of the unitary transformation corresponding to rotation or reflection. In two dimensions, an m-fold rotationally symmetric simply connected domain D can be generated by the mth-root transform of a domain, say U. We prove that the NP spectrum on D contains the NP spectrum on U counting multiplicities. We also discuss some examples including lemniscates, m-star-shaped domains, and Cassini ovals.

报告人介绍：Yong-Gwan Ji，韩国高等科学院博士后研究员，本硕博毕业于韩国仁荷大学。研究方向为谱分析，积分方程，偏微分方程的一般理论等。在Trans. Amer. Math. Soc., Math. Ann, Proc. Amer. Math. Soc, European J. Appl. Math.等国际期刊发表学术论文十余篇。主持一项韩国科学基金。

邀请人：李晓菲