The wave equation on hyperbolic spaces

2010/10/12 by Anker, Jean-Philippe, Pierfelice, Vittoria, Vallarino, Maria · 3 citations
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.2372

Abstract

In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well-posedness results for the nonlinear wave equation.

Cited by

• Decay estimates for a class of dispersive equations with partial inverse-square potentials
• Growth Estimates for Solutions to the Wave Equation on Damek--Ricci Spaces
• Local Dispersive and Strichartz estimates for the Schrödinger equation associated to the Ornstein-Uhlenbeck operator

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