Mathematische Annalen

, Volume 349, Issue 3, pp 599–622

On the dimension of divergence sets of dispersive equations


  • Juan Antonio Barceló
    • ETSI de CaminosUniversidad Politécnica de Madrid
  • Jonathan Bennett
    • School of MathematicsThe University of Birmingham
  • Anthony Carbery
    • School of Mathematics and Maxwell Institute for Mathematical SciencesThe University of Edinburgh
    • Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM

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


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.

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© Springer-Verlag 2010