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arXiv · 2211.17003

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

Lucas Vacossin
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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.

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Lucas Vacossin. 2022-11-30. Resolvent estimates in strips for obstacle scattering in 2D and local energy decay for the wave equation. https://doi.org/10.2140/paa.2023.5.1009

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