Uniform resolvent estimates for a non-dissipative Helmholtz equation

Details Uniform resolvent estimates for a non-dissipative Helmholtz equation Uniform resolvent estimates for a non-dissipative Helmholtz equation

2011-03-20

arxiv.org/abs/1103.3868v1

Physics

Mathematical Physics

Scientific paper

We study the high frequency limit for a non-dissipative Helmholtz equation. We first prove the absence of eigenvalue on the upper half-plane and close to an energy which satisfies a weak damping assumption on trapped trajectories. Then we generalize to this setting the resolvent estimates of Robert-Tamura and prove the limiting absorption principle. We finally study the semiclassical measures of the solution when the source term concentrates on a bounded submanifold of R^n.

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