Spectral Structure of Elastic Neumann-Poincare Operators

초록

In [1, 2], it is proved that the elastic Neumann-Poincare 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-Poincare operator consists of non-empty sets of eigenvalues accumulating to certain numbers determined by Lame parameters. The purpose of this paper is to review these results and their proofs, and to discuss about some questions related to these results.