The wave equation on Damek-Ricci spaces

2010/12/03 by Jean-Philippe Anker, Anker, Jean-Philippe, Vittoria Pierfelice +3 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.1012.0689

Abstract

We study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on Damek-Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global well-posedness results for the nonlinear wave equation.

Cited by

• Growth Estimates for Solutions to the Wave Equation on Damek--Ricci Spaces
• Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces

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