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

作者：D' Ancona Piero; Selberg Sigmund

来源：Journal of Differential Equations, 2012, 252(2): 1603-1634.

DOI：10.1016/j.jde.2011.03.016

• Steplike potentials
• Schrodinger equation
• Dispersive estimate

We prove a sharp dispersive estimate %26lt;br%26gt;vertical bar P(ac)u(t, x)vertical bar %26lt;= C vertical bar t vertical bar(-1/2) . vertical bar vertical bar u(0)vertical bar vertical bar L(1(R)) %26lt;br%26gt;for the one dimensional Schrodinger equation %26lt;br%26gt;iu(t) - u(xx) + V (x)u + V(0)(x) = 0, %26lt;br%26gt;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.

• 出版日期2012-1-15