Spectral analysis on the elastic Neumann-Poincaré operator (Analysis of inverse problems through partial differential equations and related topics)

Abstract

The elastic Neumann-Poincaré (eNP) operator is a boundary integral operator that appears naturally when we solve classical boundary value problems for the Lame system using layer potentials, and there is rapidly growing interest in its spectral properties recently in relation to cloaking by anomalous localized resonance (CALR). In this workshop, the speaker reported two results on the spectrum of the eNP operator. The first one is the polynomial compactness of the three-dimensional eNP operator on a C¹, α surface for a > 0, which describes a distribution of eigenvalues. The second one is on the essential spectrum of the two-dimensional eNP operator on a curve which is smooth except at a corner.