Dispersive estimate for the 1D Schrodinger equation with a steplike potential

被引：6
|
作者：
D'Ancona, Piero [1 ]
Selberg, Sigmund [2 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2012年 / 252卷 / 02期
关键词：
Steplike potentials; Schrodinger equation; Dispersive estimate; KORTEWEG-DEVRIES EQUATION; L-P-BOUNDEDNESS; INVERSE SCATTERING; WAVE-OPERATORS; LINE;
D O I：
10.1016/j.jde.2011.03.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a sharp dispersive estimate vertical bar P(ac)u(t, x)vertical bar <= C vertical bar t vertical bar(-1/2) . vertical bar vertical bar u(0)vertical bar vertical bar L(1(R)) for the one dimensional Schrodinger equation iu(t) - u(xx) + V (x)u + V(0)(x) = 0, where (1 + x(2))V E is an element of L(1) (R) and V(0) is a step function, real valued and constant on the positive and negative real axes. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：1603 / 1634
页数：32
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