IMPROVED LOCAL ENERGY DECAY FOR THE WAVE EQUATION ON ASYMPTOTICALLY EUCLIDEAN ODD DIMENSIONAL MANIFOLDS IN THE SHORT RANGE CASE

被引：3

作者：

Bony, Jean-Francois ^{[1
]}

Haefner, Dietrich ^{[2
]}

机构：

[1] Univ Bordeaux 1, CNRS, UMR 5251, Inst Math Bordeaux, F-33405 Talence, France

[2] Univ Grenoble 1, CNRS, UMR 5582, Inst Fourier, F-38402 St Martin Dheres, France

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2013年 / 12卷 / 03期

关键词：

local energy decay; resolvent smoothness; wave equation; odd dimensions; low frequencies; asymptotically Euclidean manifolds; RESONANCE; PERTURBATIONS;

D O I：

10.1017/S1474748012000801

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：635 / 650

页数：16

共 25 条

[1] CLASS OF ANALYTIC PERTURBATIONS FOR ONE-BODY SCHRODINGER HAMILTONIANS
AGUILAR, J
COMBES, JM
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1971, 22 (04) : 269 - &
[2] Alinhac S., 2010, LONDON MATH SOC LECT, V374, P118
[3] EXISTENCE OF RESONANCES IN 3 DIMENSIONS
BARRETO, AS
ZWORSKI, M
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 173 (02) : 401 - 415
[4] Bony JF, 2012, ANN SCI ECOLE NORM S, V45, P311
[5] Bony JF, 2010, MATH RES LETT, V17, P301
[6] The Semilinear Wave Equation on Asymptotically Euclidean Manifolds
Bony, Jean-Francois
Hafner, Dietrich
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (01) : 23 - 67
[7] Low Frequency Estimates and Local Energy Decay for Asymptotically Euclidean Laplacians
Bouclet, Jean-Marc
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (07) : 1239 - 1286
[8] Local energy decay of the wave equation for the exterior problem and absence of resonance in the neighborhood of the real axis
Burq, N
[J]. ACTA MATHEMATICA, 1998, 180 (01) : 1 - 29
[9] ANALYTIC CONTINUATION OF RESOLVENT KERNEL AND SCATTERING OPERATOR ASSOCIATED WITH SCHROEDINGER OPERATOR
DOLPH, CL
MCLEOD, JB
THOE, D
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1966, 16 (02) : 311 - +
[10] Spectral theory for the standard model of non-relativistic QED
Froehlich, J.
Griesemer, M.
Sigal, I. M.
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 283 (03) : 613 - 646

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