Asymptotic properties of the eigenvalues of the Neumann–Poincaré ($\operatorname {NP}
$) operator in three dimensions are treated. The region $\Omega\subset\mathbb {R}^ 3$ is …

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 …

We prove that the elastic Neumann–Poincaré (NP) operator defined on the smooth
boundary of a bounded domain in three dimensions, which is known to be non-compact, is …

We consider the conductivity transmission problem in two dimensions with a simply
connected inclusion of arbitrary shape. It is well known that the solvability of the transmission …

This is a review paper on recent development on the spectral theory of the Neumann-
Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the …

If the boundary of a domain in three dimensions is smooth enough, then the decay rate of
the eigenvalues of the Neumann-Poincaré operator is known and it is optimal. In this paper …

We consider the adjoint double layer potential (Neumann–Poincaré (NP)) operator
appearing in 3-dimensional elasticity. We show that the recent result about the polynomial …

We deduce eigenvalue asymptotics of the Neumann--Poincar\'e operators in three
dimensions. The region $\Omega $ is $ C^{2,\alpha} $($\alpha> 0$) bounded in ${\mathbf …

We deduce eigenvalue asymptotics of the Neumann–Poincaré operators in three
dimensions. The region Ω is C 2, α (α> 0) bounded in R 3 and the Neumann–Poincaré …

Abstract For the Neumann-Poincaré (double layer potential) operator in the three-
dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the …