  We prove a logarithmic local energy decay rate for the wave equation with a
wavespeed that is a compactly supported Lipschitz perturbation of unity. The
key is to establish suitable resolvent estimates at high and low energy for the
meromorphic continuation of the cutoff resolvent. The decay rate is the same as
that proved by Burq for a smooth perturbation of the Laplacian outside an
obstacle.
