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arXiv · 0905.0355

Limiting absorption principle for the dissipative Helmholtz equation

Julien Royer
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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.

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Julien Royer. 2009-05-29. Limiting absorption principle for the dissipative Helmholtz equation. https://doi.org/10.1080/03605302.2010.490287

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