On the stabilization of the elasticity system by the boundary

Abstract

We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body in R³ with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary. To do so, we use the properties of the parametrix of the Neumann operator constructed in Duke Math. J. 78 (1995), 677–714. As a consequence, we obtain time decay estimates for the local energy of the solutions of the corresponding mixed boundary value problems.