A limiting absorption principle for the Helmholtz equation with variable coefficients (Q1624164)

In this article, the limiting absorption principle is considered for an exterior Dirichlet problem for a generalized Helmholtz equation satisfying the Sommerfeld radiation condition at infinity. Precisely, the equation at hand is given by \[ \left(L+\lambda\right)v=f\,,\quad \lambda\in \mathbb{R} \] where \(L\) is a second-order elliptic operator with variable coefficients. The principal part is assumed to be a small, long range perturbation of the negative Laplacian and the lower order terms can be singular and large. The authors main tool is a sharp uniform resolvent estimate. This has applications either to the problem of embedded eigenvalues or to smoothing estimates for dispersive equations.