SPECTRAL ANALYSIS OF THE NEUMANN–POINCARÉ OPERATOR FOR THIN DOUBLY CONNECTED DOMAINS

Document Type

Article

Publication Date

1-1-2025

Abstract

We analyze the spectrum of the Neumann–Poincaré (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 an infinite-matrix representation of the NP operator involving the Grunsky coefficients of the conformal mapping and an application of the Gershgorin circle theorem. As the thickness of the domain shrinks to zero, the spectrum of the doubly connected domain approaches the interval [-1/2,1/2] in the Hausdorff distance and the density of eigenvalues approaches that of a thin circular annulus.

Publication Source (Journal or Book title)

SIAM Journal on Mathematical Analysis

First Page

2210

Last Page

2228

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