Local energy decay for Lipschitz wavespeeds
Analysis of PDEs
2018-05-08 v3
Abstract
We prove a logarithmic local energy decay rate for the wave equation with a wavespeed that is a compactly supported Lipschitz perturbation of unity. The key is to establish suitable resolvent estimates at high and low energy for the meromorphic continuation of the cutoff resolvent. The decay rate is the same as that proved by Burq for a smooth perturbation of the Laplacian outside an obstacle.
Cite
@article{arxiv.1707.06716,
title = {Local energy decay for Lipschitz wavespeeds},
author = {Jacob Shapiro},
journal= {arXiv preprint arXiv:1707.06716},
year = {2018}
}
Comments
21 pages, 3 figures