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

Lucas Vacossin

Vol. 5 (2023), No. 4, 1009–1039
Abstract

We study the problem of scattering by J strictly convex obstacles satisfying a no-eclipse condition in dimension 2. We use the result of our previous work (2022) to obtain polynomial resolvent estimates in strips below the real axis. We deduce estimates in O(|λ|log |λ|) for the truncated resolvent on the real line and give an application to the decay of the local energy for the wave equation.

Keywords
scattering resonances, spectral gap, resolvent estimates
Mathematical Subject Classification
Primary: 35J05, 35L05
Secondary: 35J10, 35S30
Milestones
Received: 16 January 2023
Revised: 13 April 2023
Accepted: 12 July 2023
Published: 15 December 2023
Authors
Lucas Vacossin
Laboratoire de Mathématiques d’Orsay
Université Paris-Saclay
UMR 8628 du CNRS
Orsay
France