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

2016/06/05 by Kazunori Ando, Hyeonbae Kang, Ando, Kazunori +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1606.01483

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.

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