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Abstract: We prove some local smoothing estimates for the Schr\-{o}dinger initial valueproblem with data in $L^2\mathbb{R}^d$, $d \geq 2$ and a general class ofpotentials. In the repulsive setting we have to assume just a power like decay$1+|x|^{-\gamma}$ for some $\gamma>0$. Also attractive perturbations areconsidered. The estimates hold for all time and as a consequence a weakdispersion of the solution is obtained. The proofs are based on similarestimates for the corresponding stationary Helmholtz equation and Kato H-smooththeory.



Author: J. A. Bercelo, A. Ruiz, L. Vega, M. C. Vilela

Source: https://arxiv.org/







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