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

页码：1603 / 1634

页数：32

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