Let P be a long range metric perturbation of the Euclidean Laplacian on ? ~d, d ≥ 2. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schr?dinger equations associated to P. The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group e ~(it,f(P)) where f has a suitable development at zero (resp. infinity).
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