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arXiv · 0802.2161

Weak Dispersive estimates for Schrödinger equations with long range potentials

J. A. Bercelo·A. Ruiz·L. Vega·M. C. Vilela
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Abstract

We prove some local smoothing estimates for the Schrödinger initial value problem with data in $L^2(\mathbb{R}^d)$, $d \geq 2$ and a general class of potentials. In the repulsive setting we have to assume just a power like decay $(1+|x|)^{-γ}$ for some $γ>0$. Also attractive perturbations are considered. The estimates hold for all time and as a consequence a weak dispersion of the solution is obtained. The proofs are based on similar estimates for the corresponding stationary Helmholtz equation and Kato H-smooth theory.

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J. A. Bercelo, A. Ruiz, L. Vega, M. C. Vilela. 2008-02-15. Weak Dispersive estimates for Schrödinger equations with long range potentials. https://arxiv.org/abs/0802.2161

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