Exponential decay estimates of the eigenvalues for the Neumann-Poincaré operator on analytic boundaries in two dimensions

Abstract

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 convergence rate is determined by the maximal Grauert radius of the boundary. We present a few examples of boundaries to show that the estimate is optimal.

12 pages, 2 figures

References in corpus (3)

• The essential spectrum of the Neumann--Poincare operator on a domain with corners
• Eigenvalues and Eigenfunctions of Double Layer Potentials
• Classification of spectra of the Neumann-Poincaré operator on planar domains with corners by resonance

Cited by in corpus (4)

• Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry
• Asymptotic behavior of spectral of Neumann-Poincare operator in Helmhotz system
• Elastic Neumann-Poincaré operators on three dimensional smooth domains: Polynomial compactness and spectral structure
• A decay estimate for the eigenvalues of the Neumann-Poincaré operator in two dimensions using the Grunsky coefficients