Abstract
We consider the Klein–Gordon equation associated with the Laplace–Beltrami operator on real hyperbolic spaces of dimension ; 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.
Citation
Jean-Philippe Anker. Vittoria Pierfelice. "Wave and Klein–Gordon equations on hyperbolic spaces." Anal. PDE 7 (4) 953 - 995, 2014. https://doi.org/10.2140/apde.2014.7.953
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