WAVE AND KLEIN-GORDON EQUATIONS ON HYPERBOLIC SPACES

被引：25
|
作者：
Anker, Jean-Philippe [1 ,2 ,3 ]
Pierfelice, Vittoria [1 ,2 ,3 ]
机构：
[1] Univ Orleans, Federat Denis Poisson FR 2964, F-45067 Orleans 2, France
[2] Univ Orleans, Lab MAPMO UMR 7349, F-45067 Orleans 2, France
[3] CNRS, F-45067 Orleans 2, France
来源：
ANALYSIS & PDE | 2014年 / 7卷 / 04期
关键词：
hyperbolic space; wave kernel; semilinear wave equation; semilinear Klein-Gordon equation; dispersive estimate; Strichartz estimate; global well-posedness; GLOBAL-SOLUTIONS; SCHRODINGER; SCATTERING; EXISTENCE;
D O I：
10.2140/apde.2014.7.953
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Klein-Gordon equation associated with the Laplace-Beltrami operator Delta on real hyperbolic spaces of dimension n >= 2; as Delta has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well-posedness results for the corresponding semilinear equation with low regularity data.
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页码：953 / 995
页数：43
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