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

초록

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