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Mathematische Annalen

, Volume 333, Issue 2, pp 271–290 | Cite as

Some remarks on the Schrödinger equation with a potential in L r t L s x

  • Piero D' AnconaEmail author
  • Vittoria Pierfelice
  • Nicola Visciglia
Article

Abstract

We study the dispersive properties of the linear Schrödinger equation with a time-dependent potential V(t,x). We show that an appropriate integrability condition in space and time on V, i.e. the boundedness of a suitable L r t L s x norm, is sufficient to prove the full set of Strichartz estimates. We also construct several counterexamples which show that our assumptions are optimal, both for local and for global Strichartz estimates, in the class of large unsigned potentials VL r t L s x .

Mathematics Subject Classification (2000)

35B40 35B25 35B65 35Q40 35Q55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Piero D' Ancona
    • 1
    Email author
  • Vittoria Pierfelice
    • 2
  • Nicola Visciglia
    • 2
  1. 1.Università di Roma “La Sapienza”Dipartimento di MatematicaRomaItaly
  2. 2.Università di PisaDipartimento di MatematicaPisaItaly

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