The Limiting Absorption Principle for Elastic Wave Propagation Problems in Perturbed Stratified Media ℝ3
Senjo Shimizu · Mathematical Methods in the Applied Sciences · 1996
We consider the self-adjoint operator governing the propagation of elastic waves in perturbed stratified media ℝ3 with free boundary–interface conditions. In this paper we establish the limiting absorption principle for this self-adjoint operator in appropriate Hilbert space. The proof of the limiting absorption principle is based on the division theorem which is proved by means of eigenfunction expansions for the self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media ℝ3.