Local energy decay for several evolution equations on asymptotically Euclidean manifolds (Q2903105)

The paper is treating the local energy decay for several evolution equations associated to long range metric perturbations of the Euclidean Laplacian: the wave, Klein-Gordon and Schrödinger equations. The study is separated by the low and, respectively, high frequency analysis. In low (respectively high) frequency, denoting by \(P\) a long range perturbation of the Euclidean Laplacian, and assuming that for the high energy part that \(P\) is non-trapping, the authors obtain a general result about the local energy decay for the group \(e^{itf(P)}\) where \(f\) has a suitable development at zero (respectively at infinity).