Workshop on Neumann-Poincare Operator and Related Topics
2019/09/26-2019/09/28

Organizer: Hyeonbae Kang, Youjun Deng

09/26星期四

14:30-18:00注册

18:00-20:00晚餐

09/27星期五

10:00-10:40, Kazunori Ando (Ehime University)

Anomalous localized resonance on the boundary with corners

11:00-11:40, Yong-Gwan Ji (Inha University)

Title: Neumann Ovaloid

Abstract: A Neumann ovaloid is a domain which generates a gravitational potential equivalent to that of two equal point masses. Explicit parameterization of a Neumann ovaloid is known only in two dimensions. Recently, Karp and Lundberg constructed a four dimensional Neumann ovaloid. In this talk, we discuss about Neumann ovaloids and related topic in neutral inclusion problem.

12:00-14:00, Lunch

14:00-14:40, Daisuke Kawagoe (Kyoto University)

Title: Spectral analysis on the elastic Neumann–Poincaré operator

Abstract:

In this talk, we see two results on spectrum of the elastic Neumann–Poincar e operator. The first one is its polynomial compactness on $C^{1, \alpha}$ surfaces. The second one is its essential spectrum on curves with a corner.

15:00-15:40, Xiaofei Li (Inha University & Zhejang University of Technology)

On the construction of weakly neutral inclusion

16:00-16:40, Yoshihisa Miyanishi (Osaka University)

Title: The spectral structure of elastic NP operators for nonhomogeneous bodies

Abstract:

We define the Neumann—Poincar\’e (NP) operator for the case of a nonhomogeneous isotropic media in 3D. Then we show that its properties depend crucially on the character of non-homogeneity. If the Lam\'e parameters are constant along the smooth boundary, the NP operator is polynomially compact. On the other hand, if these parameters are not constant, two or more intervals of continuous spectrum may appear, so the NP operator ceases to be polynomially compact. However, after a certain modification, it becomes polynomially compact again. Finally, we evaluate the rate of convergence of discrete eigenvalues of the NP operator to the tips of the essential spectrum.