Local energy decay for linear wave equations with variable coefficients (Q1779356)

For the linear wave equation with variable coefficients depending on a given differentiable function \(K(x)\) which has to satisfy some additional conditions, one considers the initial-boundary value problem with Dirichlet homogeneous data on an exterior domain with compact smooth boundary. The purpose of the paper is to derive a uniform local energy decay estimate without assuming the compactness of the support on the initial data. However the conditions imposed on \(K(x)\) are quite restrictive.