Vol. 273, No. 1, 2015

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
Maximal estimates for Schrödinger equations with inverse-square potential

Changxing Miao, Junyong Zhang and Jiqiang Zheng

Vol. 273 (2015), No. 1, 1–19
Abstract

We consider maximal estimates for the solution to an initial value problem of the linear Schrödinger equation with a singular potential. We show a result about the pointwise convergence of solutions to this special variable coefficient Schrödinger equation with initial data u0 Hs(n) for s > 1 2 or radial initial data u0 Hs(n) for s 1 4 and that the solution does not converge when s < 1 4.

Keywords
inverse square potential, maximal estimate, spherical harmonics
Mathematical Subject Classification 2010
Primary: 35B65, 35Q55, 47J35
Milestones
Received: 23 May 2013
Revised: 1 January 2014
Accepted: 25 February 2014
Published: 6 December 2014
Authors
Changxing Miao
Institute of Applied Physics and Computational Mathematics
P. O. Box 8009
Beijing, 100088
China
Junyong Zhang
Department of Mathematics
Beijing Institute of Technology
Beijing, 100081
China
Jiqiang Zheng
The Graduate School of China Academy of Engineering Physics
P. O. Box 2101
Beijing, 100088
China