Spherical perturbations of Schrodinger equations

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

Abstract

We give conditions on radial nonnegative weights W-1 and W-2 on R-n for which the a priori inequality parallel to(-Delta(S))(1/2)u parallel to(L2(W1) = 3. As a consequence we establish some new estimates for the free Schrodinger propagator e(it=Delta), which may be viewed as certain refinements of the Delta-(super)smoothness estimates of Kato and Yajima. These results, in turn, lead to the well-posedness of the initial value problem for certain time dependent first order spherical perturbations of then >= 3 dimensional Schrodinger equation.

Details

Original languageEnglish
Pages (from-to)269-290
Number of pages22
JournalJournal of Fourier Analysis and Applications
Volume12
Issue number3
Publication statusPublished - 1 Jun 2006