Spectral structure of the Neumann--Poincar\'e operator on thin domains in two dimensions

Kazunori Ando; Hyeonbae Kang; Yoshihisa Miyanishi

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arXiv · 2006.14377

Spectral structure of the Neumann--Poincar\'e operator on thin domains in two dimensions

Kazunori Ando·Hyeonbae Kang·Yoshihisa Miyanishi

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Abstract

We consider the spectral structure of the Neumann--Poincar\'e operators defined on the boundaries of thin domains of rectangle shape in two dimensions. We prove that as the aspect ratio of the domains tends to $\infty$, or equivalently, as the domains get thinner, the spectra of the Neumann--Poincar\'e operators are densely distributed in the interval $[-1/2,1/2]$.

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Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi. 2020-06-25. Spectral structure of the Neumann--Poincar\'e operator on thin domains in two dimensions. https://arxiv.org/abs/2006.14377

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