Smoothing property for Schrodinger equations with potential superquadraticat infinity

Authors
Yajima, K Zhang, GP
Citation
K. Yajima et Gp. Zhang, Smoothing property for Schrodinger equations with potential superquadraticat infinity, COMM MATH P, 221(3), 2001, pp. 573-590
Citations number
31
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
221
Issue
3
Year of publication
2001
Pages
573 - 590
Database
ISI
SICI code
0010-3616(200108)221:3<573:SPFSEW>2.0.ZU;2-Q
Abstract
We prove a smoothing property for one dimensional time dependent Schrodinge r equations with potentials which satisfy V(x) similar to C\x\(k) at infini ty, k > 2. As an application, we show that the initial value problem for ce rtain nonlinear Schrodinger equations with such potentials is L-2 well-pose d. We also prove a sharp asymptotic estimate of the L-p-norm of the normali zed eigenfunctions of H = -Delta + V for large energy.