# Wave and Klein-Gordon equations on hyperbolic spaces

Abstract : We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; 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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https://hal.archives-ouvertes.fr/hal-00581773
Contributor : Jean-Philippe Anker <>
Submitted on : Saturday, July 6, 2013 - 11:04:09 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Long-term archiving on: : Monday, October 7, 2013 - 3:00:15 AM

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### Citation

Jean-Philippe Anker, Vittoria Pierfelice. Wave and Klein-Gordon equations on hyperbolic spaces. Analysis & PDE, Mathematical Sciences Publishers, 2014, 7 (4), pp.953-995. ⟨10.2140/apde.2014.7.953⟩. ⟨hal-00581773v2⟩

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