Resolvent estimates for normally hyperbolic trapped sets

Details Resolvent estimates for normally hyperbolic trapped sets Resolvent estimates for normally hyperbolic trapped sets

2010-03-24

arxiv.org/abs/1003.4640v4

Mathematics

Analysis of PDEs

Correction of further small errors, including confusing notation in commutator argument. To appear in Ann. Henri Poincare

Scientific paper

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.

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