Elastic Neumann-Poincaré operators on three dimensional smooth domains: Polynomial compactness and spectral structure

Abstract

We prove that the elastic Neumann--Poincaré operator defined on the smooth boundary of a bounded domain in three dimensions, which is known to be non-compact, is in fact polynomially compact. As a consequence, we prove that the spectrum of the elastic Neumann-Poincaré operator consists of three non-empty sequences of eigenvalues accumulating to certain numbers determined by Lamé parameters. These results are proved using the surface Riesz transform, calculus of pseudo-differential operators and the spectral mapping theorem.

14 pages

References in corpus (2)

• Spectral resolution of the Neumann-Poincaré operator on intersecting disks and analysis of plasmon resonance
• Eigenvalues and Eigenfunctions of Double Layer Potentials