Uniform resolvent estimates for a non-dissipative Helmholtz equation

2011/03/20 by Julien Royer, Royer, Julien
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1103.3868

Abstract

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 Rⁿ.

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