Local smoothing for scattering manifolds with hyperbolic trapped sets
Analysis of PDEs
2012-06-06 v3 Mathematical Physics
math.MP
Abstract
We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the trapped region, a result of Burq and Cardoso-Vodev to provide an estimate near infinity, and the microlocal calculus on scattering manifolds to combine the two.
Cite
@article{arxiv.0712.3237,
title = {Local smoothing for scattering manifolds with hyperbolic trapped sets},
author = {Kiril Datchev},
journal= {arXiv preprint arXiv:0712.3237},
year = {2012}
}
Comments
16 pages. Published version available at http://www.springerlink.com/content/r663321331243288/?p=5ad2fe4778a742e4949de2030a409358&pi=11