Local energy decay for Lipschitz wavespeeds
Local energy decay for Lipschitz wavespeeds
复制标题
Lipschitz 波速的局部能量衰减
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Jacob Shapiro
中科院分区：
文献类型：
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作者：
Jacob Shapiro
摘要本文证明了波速为紧支撑的Lipschitz单位扰动的波动方程的对数局部能量衰减率。关键是建立适当的预解式估计在高，低能量的亚纯延拓截断预解式。的衰减率是相同的证明由伯克的光滑扰动的拉普拉斯算子外的障碍。
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.