Uniform resolvent estimates for a non-dissipative Helmholtz equation
Mathematical Physics
2011-03-23 v1 Analysis of PDEs
math.MP
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 R^n.
Cite
@article{arxiv.1103.3868,
title = {Uniform resolvent estimates for a non-dissipative Helmholtz equation},
author = {Julien Royer},
journal= {arXiv preprint arXiv:1103.3868},
year = {2011}
}