On the region free from the poles of the resolvent for the elastic wave equation with the Neumann boundary condition (Q1327775)

This brief note considers an isotropic wave equation in an exterior domain of \(\mathbb{R}^ 3\) subject to a Neumann condition on the boundary. It is well known that a Rayleigh wave propagates along the surface in such conditions, and this in turn suggests that the poles of this body surface wave must lie on the real axis. This conjecture is proved in outline and a detailed proof is promised in a forthcoming paper.