Spectral analysis of the Neumann--Poincaré operator on the crescent-shaped domain and touching disks and analysis of plasmon resonance

2018/10/30 by Younghoon Jung, Mikyoung Lim, Jung, Younghoon +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1810.12486

openalex publication_date 2018/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Neumann--Poincaré 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 the operator via the Fourier transform on the boundary circles of the domain. In particular, we define a Hilbert space on which the operator is bounded, self-adjoint. We then obtain the complete spectral resolution of the Neumann--Poincaré operator. On both the crescent-shaped domain and touching disks, the Neumann--Poincaré operator has only absolutely continuous spectrum on the closed interval [-1/2,1/2]. As an application, we analyze the plasmon resonance on the crescent-shaped domain and touching disks.

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