Semiclassical measure for the solution of the dissipative Helmholtz equation

We study the semiclassical measure for the solution of the high-frequency Helmholtz equation in with non-constant absorption index and a source term concentrated on a bounded submanifold of . The potential is not assumed to be non-trapping, but trapped trajectories have to go through the region where the absorption index is positive. In that case, the solution is microlocally written around any point away from the source as a sum (finite or infinite) of lagrangian distributions.