Small Time Behavior and Summability for the Schrödinger Equation

Brian Choi – GJM, Volume 6, Issue 2 (2021), 9-21.

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janvier 4, 2022
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We consider the Carleson’s problem regarding small time almost everywhere convergence to initial data for the Schrödinger equation, both linear and nonlinear on $\mathbb{R}$ . It is shown, via the smoothing effect of the Schrödinger flow, that the (sharp) result proved by Dahlberg and Kenig for initial data in Sobolev spaces still holds when one considers the full Schrödinger equation with a certain class of potentials. As for $s<\frac{1}{4},$ the failure of $L^p$ -boundedness of the (localized) maximal operator is investigated.

Categories: Issue2

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Received: August 6, 2020
Accepted: October 26, 2021
Published online: December 30, 2021

Authors:

Brian Choi
Department of Mathematics and Statistics,
Boston University,
111 Cummington Mall, Boston, 02215, MA, USA

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