Ricerc@Sapienza

We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain
with Dirichlet boundary conditions:
egin{equation*}
(L+lambda)v=f,
qquad
lambdain 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.