Local energy decay for several evolution equations on asymptotically euclidean manifolds

Jean-François Bony; Dietrich Häfner

Annales scientifiques de l'École Normale Supérieure (2012)

  • Volume: 45, Issue: 2, page 311-335
  • ISSN: 0012-9593

Abstract

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Let  P be a long range metric perturbation of the Euclidean Laplacian on  ℝ d , d ≥ 2 . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger 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 i t f ( P ) where f has a suitable development at zero (resp. infinity).

How to cite

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Bony, Jean-François, and Häfner, Dietrich. "Local energy decay for several evolution equations on asymptotically euclidean manifolds." Annales scientifiques de l'École Normale Supérieure 45.2 (2012): 311-335. <http://eudml.org/doc/272226>.

@article{Bony2012,
abstract = {Let $P$ be a long range metric perturbation of the Euclidean Laplacian on $\{\mathbb \{R\}\}^d$, $d \ge 2$. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger 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 $e^\{i t f(P)\}$ where $f$ has a suitable development at zero (resp. infinity).},
author = {Bony, Jean-François, Häfner, Dietrich},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {local energy decay; low frequencies; asymptotically euclidean manifolds; Mourre theory},
language = {eng},
number = {2},
pages = {311-335},
publisher = {Société mathématique de France},
title = {Local energy decay for several evolution equations on asymptotically euclidean manifolds},
url = {http://eudml.org/doc/272226},
volume = {45},
year = {2012},
}

TY - JOUR
AU - Bony, Jean-François
AU - Häfner, Dietrich
TI - Local energy decay for several evolution equations on asymptotically euclidean manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2012
PB - Société mathématique de France
VL - 45
IS - 2
SP - 311
EP - 335
AB - Let $P$ be a long range metric perturbation of the Euclidean Laplacian on ${\mathbb {R}}^d$, $d \ge 2$. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger 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 $e^{i t f(P)}$ where $f$ has a suitable development at zero (resp. infinity).
LA - eng
KW - local energy decay; low frequencies; asymptotically euclidean manifolds; Mourre theory
UR - http://eudml.org/doc/272226
ER -

References

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