  We prove local energy decay for the damped wave equation on R^d. The problem
which we consider is given by a long range metric perturbation of the Euclidean
Laplacian with a short range absorption index. Under a geometric control
assumption on the dissipation we obtain an almost optimal polynomial decay for
the energy in suitable weighted spaces. The proof relies on uniform estimates
for the corresponding "resolvent", both for low and high frequencies. These
estimates are given by an improved dissipative version of Mourre's commutators
method.
