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We consider the spectral structure of the Neumann--Poincare 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--Poincare operators are densely distributed in the interval $[-1/2,1/2]$.
We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincare operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a property. It is do
This is a survey of accumulated spectral analysis observations spanning more than a century, referring to the double layer potential integral equation, also known as Neumann-Poincare operator. The very notion of spectral analysis has evolved along th
We prove that the elastic Neumann--Poincare operator defined on the smooth boundary of a bounded domain in three dimensions, which is known to be non-compact, is in fact polynomially compact. As a consequence, we prove that the spectrum of the elasti
The elastic Neumann--Poincare operator is a boundary integral operator associated with the Lame system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two different points d
The Neumann-Poincare operator is a boundary-integral operator associated with harmonic layer potentials. This article proves the existence of eigenvalues within the essential spectrum for the Neumann-Poincare operator for certain Lipschitz curves in