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The wave equation on Damek–Ricci spaces

  • Jean-Philippe Anker
  • Vittoria Pierfelice
  • Maria VallarinoEmail author
Article

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.

Keywords

Damek–Ricci spaces Semilinear wave equation Dispersive estimate Strichartz estimate Global well-posedness 

Mathematics Subject Classification (2010)

35L05 43A85 58J45 22E30 35L71 43A90 47J35 58D25 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jean-Philippe Anker
    • 1
  • Vittoria Pierfelice
    • 1
  • Maria Vallarino
    • 2
    Email author
  1. 1.CNRS, Fédération Denis Poisson (FR 2964), Laboratoire MAPMO (UMR 6628)Université d’OrléansOrléans Cedex 2France
  2. 2.Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”Politecnico di TorinoTorinoItaly

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