17 citations · 70 across the 20 of their papers we have counts for
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Generic properties of the Neumann-Poincaré operator: simplicity of eigenvalues and cyclic vectors
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi +1
Two generic properties of the Neumann--Poincaré operator are investigated. We prove that non-zero eigenvalues of the Neumann--Poincaré operator on smooth boundaries in three dimens…
A remark on decay rates of odd partitions: An application of spectral asymptotics of the Neumann--Poincaré operators
Yoshihisa Miyanishi
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…
Decay rate of the eigenvalues of the Neumann-Poincaré operator
Shota Fukushima, Hyeonbae Kang, Yoshihisa Miyanishi
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,…
Spectral structure of the Neumann-Poincaré operator on thin ellipsoids and flat domains
Kazunori Ando, Hyeonbae Kang, Sanghyuk Lee +1
We investigate the spectral structure of the Neumann-Poincaré operator on thin ellipsoids. Two types of thin ellipsoids are considered: long prolate ellipsoids and flat oblate elli…
Spectral structure of the Neumann--Poincaré operator on thin domains in two dimensions
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi
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 ra…
Spectral analysis of Neumann-Poincaré operator
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi +1
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-Poinca…
Spectral properties of the Neumann-Poincaré operator in 3D elasticity
Yoshihisa Miyanishi, Grigori Rozenblum
We consider the double layer potential (Neumann-Poincaré) operator appearing in 3-dimensional elasticity. We show that the recent result about the polynomial compactness of this op…
Convergence rate for eigenvalues of the elastic Neumann--Poincaré operator on smooth and real analytic boundaries in two dimensions
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi
The elastic Neumann--Poincaré operator is a boundary integral operator associated with the Lamé system of linear elasticity. It is known that if the boundary of a planar domain is…
Spectral structure of the Neumann--Poincaré operator on tori
Kazunori Ando, Yong-Gwan Ji, Hyeonbae Kang +2
We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincaré operator defined on its boundary has infinitely many negative eigenvalue…
Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry
Yoshihisa Miyanishi
We deduce eigenvalue asymptotics of the Neumann--Poincaré operators in three dimensions. The region is () bounded in and the Neumann--Poincaré o…
The first Hadamard variation of Neumann-Poincaré eigenvalues on the sphere
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi +1
The Neumann-Poincaré operator on the sphere has , , as its eigenvalues and the corresponding multiplicity is . We consider the bifurcation…
Elastic Neumann-Poincaré operators on three dimensional smooth domains: Polynomial compactness and spectral structure
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi
We prove that the elastic Neumann--Poincaré operator defined on the smooth boundary of a bounded domain in three dimensions, which is known to be non-compact, is in fact polynomial…
Exponential decay estimates of the eigenvalues for the Neumann-Poincaré operator on analytic boundaries in two dimensions
Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi
We show that the eigenvalues of the Neumann-Poincaré operator on analytic boundaries of simply connected bounded planar domains tend to zero exponentially fast, and the exponential…
Eigenvalues and Eigenfunctions of Double Layer Potentials
Yoshihisa Miyanishi, Takashi Suzuki
For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfu…