MathSciDoc: An Archive for Mathematician ∫

Index	Title	Upload Time	Modified Time
1	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 [ Download ] [ 2018-10-31 04:30:06 uploaded by xmdu1989 ] [ 993 downloads ] [ 0 comments ] Abstract × 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. OK [ Abstract ] [ Full ] Please log in for comment!	2018-10-31 04:30:06	-