Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$

Details Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$ Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$

2010-11-17

arxiv.org/abs/1011.3919v2

Mathematics

Analysis of PDEs

34 pages; another appendix is added; some changes are made in the proof in the even dimensional case

Scientific paper

We prove optimal dispersive estimates for the wave group
$e^{it\sqrt{-\Delta+V}}$ for a class of real-valued potentials $V\in
C^{(n-3)/2}({\bf R}^n)$, $4\le n\le 7$, such that $\partial_x^\alpha
V(x)=O(|x|^{-\delta})$ for $|x|>1$, where $\delta>(n+1)/2$.

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