Spectral Structure of Elastic Neumann–Poincaré Operators

In [1, 2], it is proved that the elastic Neumann–Poincaré operator defined on the smooth boundary of a bounded domain, which is known to be non-compact, is in fact polynomially compact. As a consequence, it is shown that the spectrum of the elastic Neumann-Poincaré operator consists of non-empty sets of eigenvalues accumulating to certain numbers determined by Lamé parameters. The purpose of this paper is to review these results and their proofs, and to discuss about some questions related to these results.