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Spectral structure of the Neumann–Poincaré operator on thin domains in two dimensions


We consider the spectral structure of the Neumann–Poincaré operators defined on the boundaries of thin domains of rectangular shape in two dimensions. We prove that as the aspect ratio of the domains tends to ∞, or equivalently, as the domains get thinner, the spectra of the Neumann–Poincaré operators are densely distributed in [−1/2, 1/2], the interval which contains the spectrum of Neumann–Poincaré operators.

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We thank the anonymous referee for helpful comments on this paper.

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Correspondence to Hyeonbae Kang.

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This work was supported by NRF (of S. Korea) grants No. 2019R1A2B5B01069967 and by JSPS (of Japan) KAKENHI Grant Number JP19K14553, 20K03655 and 21K13805.

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Ando, K., Kang, H. & Miyanishi, Y. Spectral structure of the Neumann–Poincaré operator on thin domains in two dimensions. JAMA 146, 791–800 (2022).

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