  We prove smoothing estimates in Morrey-Campanato spaces for a Helmholtz
equation $$
  -Lu+zu=f,
  \qquad
  -Lu:=\nabla^{b}(a(x)\nabla^{b}u)-c(x)u,
  \qquad
  \nabla^{b}:=\nabla+ib(x) $$ with fully variable coefficients, of limited
regularity, defined on the exterior of a starshaped compact obstacle in
$\mathbb{R}^{n}$, $n\ge3$, with Dirichlet boundary conditions. The principal
part of the operator is a long range perturbation of a constant coefficient
operator, while the lower order terms have an almost critical decay. We give
explicit conditions on the size of the perturbation which prevent trapping.
  As an application, we prove smoothing estimates for the Schr\"{o}dinger flow
$e^{itL}$ and the wave flow $e^{it \sqrt{L}}$ with variable coefficients on
exterior domains and Dirichlet boundary conditions.
