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arXiv · 1612.08946

A sharp Schrodinger maximal estimate in $\mathbb{R}^2$

Xiumin Du·Larry Guth·Xiaochun Li
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Abstract

We show that $\lim_{t \to 0} e^{itΔ}f(x) = f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ provided that $s>1/3$. This result is sharp up to the endpoint. The proof uses polynomial partitioning and decoupling.

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Xiumin Du, Larry Guth, Xiaochun Li. 2017-06-20. A sharp Schrodinger maximal estimate in $\mathbb{R}^2$. https://arxiv.org/abs/1612.08946

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