Series Expansions of the Layer Potential Operators Using the Faber Polynomials and Their Applications to the Transmission Problem

DOI10.1137/20M1348698zbMath1465.35127OpenAlexW3138056835MaRDI QIDQ5858116

Younghoon Jung, Mikyoung Lim

Publication date: 9 April 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1348698

zbMATH Keywords

Neumann-Poincaré operatorfinite section methodplasmonic resonancegeometric function theoryconductivity transmission problem

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral operators (45P05)

Related Items (max. 100)

Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials ⋮ Approximate method for solving the problem of conformal mapping of an arbitrary polygon to a unit circle ⋮ Spectral properties of the Neumann-Poincaré operator on rotationally symmetric domains ⋮ Geometric multipole expansion and its application to semi-neutral inclusions of general shape ⋮ Inverse Problem for a Planar Conductivity Inclusion ⋮ Explicit analytic solution for the plane elastostatic problem with a rigid inclusion of arbitrary shape subject to arbitrary far-field loadings ⋮ A decay estimate for the eigenvalues of the Neumann-Poincaré operator using the Grunsky coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving integral equations on piecewise smooth boundaries using the RCIP method: a tutorial
• Mathematical and statistical methods for multistatic imaging
• The essential spectrum of the Neumann-Poincaré operator on a domain with corners
• Analytical shape recovery of a conductivity inclusion based on Faber polynomials
• Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann-Poincaré operator
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Compact linear operators on functional spaces with two norms
• Exponential decay estimates of the eigenvalues for the Neumann-Poincaré operator on analytic boundaries in two dimensions
• Spectral permanence in a space with two norms
• Shape reconstruction of nanoparticles from their associated plasmonic resonances
• Polynomials orthogonal over a region and Bieberbach polynomials
• Reconstruction of small inhomogeneities from boundary measurements
• Transmission problems and spectral theory for singular integral operators on Lipschitz domains
• Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking due to anomalous localized resonance
• An extension of the Eshelby conjecture to domains of general shape in anti-plane elasticity
• Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum
• Spectral bounds for the Neumann-Poincaré operator on planar domains with corners
• Embedded eigenvalues for the Neumann-Poincaré operator
• Characterization of the essential spectrum of the Neumann-Poincaré operator in 2D domains with corner via Weyl sequences
• Classification of spectra of the Neumann-Poincaré operator on planar domains with corners by resonance
• Poincaré's variational problem in potential theory
• Spectral resolution of the Neumann-Poincaré operator on intersecting disks and analysis of plasmon resonance
• The Fredholm eigenvalues of plane domains
• Fredholm eigenvalues of multiply-connected domains
• Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen
• Spectral properties of the Neumann–Poincaré operator and uniformity of estimates for the conductivity equation with complex coefficients
• Controlling Electromagnetic Fields
• Optimal Shape Design by Partial Spectral Data
• On the cloaking effects associated with anomalous localized resonance
• On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries
• Regularity Properties of Solutions to Transmission Problems
• Conformal Mapping via a Density Correspondence for the Double-Layer Potential
• Corner Effects on the Perturbation of an Electric Potential
• The Plasmonic Resonances of a Bowtie Antenna
• A decay estimate for the eigenvalues of the Neumann-Poincaré operator using the Grunsky coefficients
• Eigenvalues and eigenfunctions of double layer potentials
• The Osgood-Taylor-Caratheodory Theorem
• Linear integral equations
• Approximation of approximation numbers by truncation
• Symmetry of a boundary integral operator and a characterization of a ball

This page was built for publication: Series Expansions of the Layer Potential Operators Using the Faber Polynomials and Their Applications to the Transmission Problem