A Sharp Schrödinger Maximal Estimate in R^2

Xiumin Du University of Maryland College Park Larry Guth Massachusetts Institute of Technology Xiaochun Li University of Illinois at Urbana-Champaign

Classical Analysis and ODEs mathscidoc:1810.05001

Distinguished Paper Award in 2018

Ann. of Math. (2), 186, (2), 607-640, 2017.8
We show that $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ 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.
restriction, Schrödinger equation, Schrödinger maximal function, polynomial partitioning, decoupling
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  title={A Sharp Schrödinger Maximal Estimate in R^2},
  author={Xiumin Du, Larry Guth, and Xiaochun Li},
  booktitle={Ann. of Math. (2)},
Xiumin Du, Larry Guth, and Xiaochun Li. A Sharp Schrödinger Maximal Estimate in R^2. 2017. Vol. 186. In Ann. of Math. (2). pp.607-640. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181031043006873368171.
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