Resolvent and Strichartz estimates for elastic wave equations

Abstract

We show a simple argument to prove resolvent estimates for Lamé operators of elasticity, with constant coefficients, and Strichartz estimates for the associated elastic wave equation. The argument is based on the Helmholtz decomposition for vector fields and some elliptic regularity result in weighted L 2 -spaces. By standard perturbation arguments, we can include small critical 0-order potentials in the main results.