| Abstract: | In this article the analytic and asymptotic properties of the resolvent for elastic waves in a three dimensional domain perturbed from the isotropic half space R 3+ are studied. In this case, the asymptotic expansion of the resolvent at the origin has logarithmic terms. This property is totally different from the case of the whole 3‐dimensional space. The existence of the surface waves like the Rayleigh waves makes this difference. As an application of the asymptotic properties of the resolvent, the rate of the local energy decay estimates for the dynamical equations is obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
