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

Abstract

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.

References in corpus (2)

• Spectral problems in open quantum chaos
• From open quantum systems to open quantum maps

Cited by in corpus (1)

• The fractal uncertainty principle via Dolgopyat's method in higher dimensions