We prove a sharp dispersive estimate|Pacu(t,x)|≤C|t|-1/2{dot operator}{norm of matrix}u(0){norm of matrix}L1(R) for the one dimensional Schrödinger equationiut-uxx+V(x)u+V0(x)u=0, where (1+x2)V∈L1(R) and V0 is a step function, real valued and constant on the positive and negative real axes. © 2011 Elsevier Inc.
Dispersive estimate for the 1D Schrödinger equation with a steplike potential / D'Ancona, Piero Antonio; S., Selberg. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 252:2(2012), pp. 1603-1634. [10.1016/j.jde.2011.03.016]
Dispersive estimate for the 1D Schrödinger equation with a steplike potential
D'ANCONA, Piero Antonio;
2012
Abstract
We prove a sharp dispersive estimate|Pacu(t,x)|≤C|t|-1/2{dot operator}{norm of matrix}u(0){norm of matrix}L1(R) for the one dimensional Schrödinger equationiut-uxx+V(x)u+V0(x)u=0, where (1+x2)V∈L1(R) and V0 is a step function, real valued and constant on the positive and negative real axes. © 2011 Elsevier Inc.File allegati a questo prodotto
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