Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation

In this note, we are interested in the problem of scattering by J strictly convex obstacles satisfying a no-eclipse condition in dimension 2. We use the result of a previous article of the author to obtain polynomial resolvent estimates in strips below the real axis. We deduce estimates in O(|$\lambda$| log |$\lambda$|) for the truncated resolvent on the real line and give an application to the decay of the local energy for the wave equation.