Limiting absorption principle for the dissipative Helmholtz equation
Analysis of PDEs
2014-03-04 v2
Abstract
Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolvent estimates for the high frequency Helmholtz equation when trapped trajectories meet the set where the imaginary part of the potential is non-zero. We also give the resolvent estimates in Besov spaces.
Cite
@article{arxiv.0905.0355,
title = {Limiting absorption principle for the dissipative Helmholtz equation},
author = {Julien Royer},
journal= {arXiv preprint arXiv:0905.0355},
year = {2014}
}