Related papers: Geometric series expansion of the Neumann-Poincar\…
We represent a matrix representation of the Neumann-Poincar\'e operator defined on the boundaries of a torus. A torus is a doubly connected domain in three dimensions. There is a well-known parametrization for the shape of the torus, the…
The Neumann-Poincar\'e (NP) operator naturally appears in the context of metamaterials as it may be used to represent the solutions of elliptic transmission problems via potentiel theory. In particular, its spectral properties are closely…
This paper concerns the eigenvalues of the Neumann-Poincar\'e operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and…
We consider the Neumann--Poincar\'{e} operator on a planar domain enclosed by two touching circular boundaries. This domain, which is a crescent-shaped domain or touching disks, has a cusp at the touching point of two circles. We analyze…
We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Neumann-Poincar{\'e} operators. These classes of domains…
We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\mathbb{R}^d$ and characterize solvability of the problem in terms of the…
The boundary double layer potential, or the Neumann-Poincare operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the…
The Neumann-Poincar\'e 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-Poincar\'e operator for certain…
The elastic Neumann--Poincar\'e operator is a boundary integral operator associated with the Lam\'e system of linear elasticity. It is known that if the boundary of a planar domain is smooth enough, it has eigenvalues converging to two…
We analyze the spectrum of the Neumann-Poincar\'e (NP) operator for a doubly connected domain lying between two level curves defined by a conformal mapping, where the inner boundary of the domain is of general shape. The analysis relies on…
We prove that the elastic Neumann--Poincar\'e 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…
It is known that the Neumann--Poincar\'e operator for the Lam\'e system of linear elasticity is polynomially compact and, as a consequence, that its spectrum consists of three non-empty sequences of eigenvalues accumulating to certain…
The purpose of this paper is to investigate the spectral nature of the Neumann-Poincar\'e operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which…
We prove the convergence of layer potential operators for the harmonic transmission problem over a sequence of converging two-sided extension domains. Consequently, the Neumann-Poincar{\'e} operators, Calder{\'o}n projectors, and associated…
We consider Calder{\'o}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{\'e}-Steklov (Dirichlet-to-Neumann) operator for the conductivity problem on such…
We introduce a theorem currently proved unique by the asymptotic behaviors of eigenvalues of a compact operator. Specifically, a problem of partitions is considered and the Neumann--Poincar\'e operator is employed as the compact linear…
We consider the spectral structure of the Neumann--Poincar\'e 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…
We investigate the decay property of the eigenvalues of the Neumann-Poincar\'{e} operator in two dimensions. As is well-known, this operator admits only a sequence of eigenvalues that accumulates to zero as its spectrum for a bounded domain…
This paper concerns the spectral properties of the Neumann-Poincar\'e operator on $m$-fold rotationally symmetric planar domains. An $m$-fold rotationally symmetric simply connected domain $D$ is realized as the $m$th-root transform of a…
We consider the double layer potential (Neumann-Poincar\'e) operator appearing in 3-dimensional elasticity. We show that the recent result about the polynomial compactness of this operator for the case of a homogeneous media follows without…