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.
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Communicated by P. Constantin
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Datchev, K. Local Smoothing for Scattering Manifolds with Hyperbolic Trapped Sets. Commun. Math. Phys. 286, 837–850 (2009). https://doi.org/10.1007/s00220-008-0684-1
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DOI: https://doi.org/10.1007/s00220-008-0684-1