On the dimension of divergence sets of dispersive equations

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Authors

Colleges, School and Institutes

Abstract

We refine results of Carleson, Sjogren and Sjolin regarding the pointwise convergence to the initial data of solutions to the Schrodinger equation. We bound the Hausdorff dimension of the sets on which convergence fails. For example, with initial data in, the sets of divergence have dimension at most one.

Details

Original languageEnglish
Pages (from-to)599-622
Number of pages24
JournalMathematische Annalen
Volume349
Issue number3
Publication statusPublished - 1 Mar 2011