A Note on Decay Rates of the Local Energy for Wave Equations with Lipschitz Wavespeeds

Abstract

We consider the Cauchy problem for wave equations with variable coefficients in the whole space. We improve the rate of decay of the local energy, which has been recently studied by J. Shapiro, where he derives the log-order decay rates of the local energy under stronger assumptions on the regularity of the initial data.

12 pages