TY - JOUR
T1 - Spherical perturbations of Schrodinger equations
AU - Barceló, JA
AU - Bennett, Jonathan
AU - Ruiz, A
PY - 2006/6/1
Y1 - 2006/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33646884191&partnerID=8YFLogxK
U2 - 10.1007/s00041-006-6003-3
DO - 10.1007/s00041-006-6003-3
M3 - Article
VL - 12
SP - 269
EP - 290
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
IS - 3
ER -