Local energy decay for Lipschitz wavespeeds

Jacob Shapiro

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arXiv · 1707.06716

Local energy decay for Lipschitz wavespeeds

Jacob Shapiro

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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.

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Jacob Shapiro. 2017-07-20. Local energy decay for Lipschitz wavespeeds. https://arxiv.org/abs/1707.06716

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