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

2020/06/25 by Ando, Kazunori, Kang, Hyeonbae, Miyanishi, Yoshihisa
#35J47 #35P05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2006.14377

Abstract

We consider the spectral structure of the Neumann--Poincaré 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 ∞, or equivalently, as the domains get thinner, the spectra of the Neumann--Poincaré operators are densely distributed in the interval [-1/2,1/2].

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