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Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case

Published online by Cambridge University Press:  13 July 2012

Jean-François Bony
Affiliation:
Institut de Mathématiques de Bordeaux, UMR 5251 du CNRS, Université de Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France (bony@math.u-bordeaux1.fr)
Dietrich Häfner
Affiliation:
Université de Grenoble 1, Institut Fourier, UMR 5582 du CNRS, BP 74, 38402 St Martin d’Hères, France (Dietrich.Hafner@ujf-grenoble.fr)

Abstract

We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give estimates of powers of the resolvent of the wave propagator between weighted spaces.

Type
Research Article
Copyright
©Cambridge University Press 2012 

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