Mathematische Annalen

, Volume 349, Issue 3, pp 599–622

On the dimension of divergence sets of dispersive equations

  • Juan Antonio Barceló
  • Jonathan Bennett
  • Anthony Carbery
  • Keith M. Rogers
Article

DOI: 10.1007/s00208-010-0529-z

Cite this article as:
Barceló, J.A., Bennett, J., Carbery, A. et al. Math. Ann. (2011) 349: 599. doi:10.1007/s00208-010-0529-z

Abstract

We refine results of Carleson, Sjögren and Sjölin regarding the pointwise convergence to the initial data of solutions to the Schrödinger equation. We bound the Hausdorff dimension of the sets on which convergence fails. For example, with initial data in \({H^1(\mathbb{R}^{3})}\), the sets of divergence have dimension at most one.

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Juan Antonio Barceló
    • 1
  • Jonathan Bennett
    • 2
  • Anthony Carbery
    • 3
  • Keith M. Rogers
    • 4
  1. 1.ETSI de CaminosUniversidad Politécnica de MadridMadridSpain
  2. 2.School of MathematicsThe University of BirminghamBirminghamUK
  3. 3.School of Mathematics and Maxwell Institute for Mathematical SciencesThe University of EdinburghEdinburghUK
  4. 4.Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCMMadridSpain