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arXiv · 1703.01360

A note on pointwise convergence for the Schrödinger equation

Renato Lucà·Keith Rogers
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Abstract

We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain recently proved that there is initial data, in $H^s(\mathbb{R}^n)$ with $s<\frac{n}{2(n+1)}$, for which the solution diverges on a set of nonzero Lebesgue measure. We provide a different example enabling the generalisation to fractional Hausdorff measure.

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Renato Lucà, Keith Rogers. 2017-03-03. A note on pointwise convergence for the Schrödinger equation. https://doi.org/10.1017/s0305004117000743

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