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

Fernando Cardoso; Georgi Vodev

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

Analysis of PDEs 2010-12-07 v2

Authors: Fernando Cardoso , Georgi Vodev

Abstract

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 $\delta>(n+1)/2$ .

Keywords

dispersive estimates wave equation wave group real-valued potentials optimal estimates

Cite

@article{arxiv.1011.3919,
  title  = {Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$},
  author = {Fernando Cardoso and Georgi Vodev},
  journal= {arXiv preprint arXiv:1011.3919},
  year   = {2010}
}

Comments

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

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