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This content will become publicly available on June 30, 2026

Title: Spectral Analysis of the Neumann–Poincaré Operator for Thin Doubly Connected Domains
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.  more » « less
Award ID(s):
2206037
PAR ID:
10611655
Author(s) / Creator(s):
; ;
Publisher / Repository:
SIAM
Date Published:
Journal Name:
SIAM Journal on Mathematical Analysis
Volume:
57
Issue:
3
ISSN:
0036-1410
Page Range / eLocation ID:
2210 to 2228
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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