Abstract
We prove local smoothing estimates for the Schrödinger initial value problem with data in the energy space L 2(ℝ d ), d ≥ 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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