Wave and Klein–Gordon equations on hyperbolic spaces

Jean-Philippe Anker, Vittoria Pierfelice

Type: Article

Publication Date: 2014-08-27

Citations: 30

DOI: https://doi.org/10.2140/apde.2014.7.953

Abstract

We consider the Klein-Gordon equation associated with the Laplace-Beltrami operator on real hyperbolic spaces of dimension n 2; as 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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