A limiting absorption principle for the Helmholtz equation with variable   coefficients
  We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain with Dirichlet boundary conditions \begin{equation*}   (L+\lambda)v=f,   \qquad   \lambda\in \mathbb{R}   \end{equation*} under a Sommerfeld radiation condition at infinity. The operator $L$ is a second order elliptic operator with variable coefficients, the principal part is a small, long range perturbation of $-\Delta$, while lower order terms can be singular and large. The main tool is a sharp uniform resolvent estimate, which has independent applications to the problem of embedded eigenvalues and to smoothing estimates for dispersive equations. 
Federico Cacciafesta, Piero D'Ancona, Renato Luc\`a
math.AP