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arXiv · 1506.05325

An improved necessary condition for the Schr\"odinger maximal estimate

Renato Lucà·Keith Rogers
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Abstract

We improve the necessary condition for Carleson's problem regarding convergence for the Schr\"odinger equation in dimensions $n\ge 3$. We prove that if the solution converges almost everywhere to its initial datum as time tends to zero, for all data in $H^s(\mathbb{R}^n)$, then $s\ge \frac{n}{2(n+2)}$.

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Renato Lucà, Keith Rogers. 2015-06-17. An improved necessary condition for the Schr\"odinger maximal estimate. https://arxiv.org/abs/1506.05325

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