  Let ${\cal A}(x;D_x)$ be a second-order linear differential operator in
divergence form. We prove that the operator ${\l}I- {\cal A}(x;D_x)$, where
$\l\in\csp$ and $I$ stands for the identity operator, is closed and injective
when ${\rm Re}\l$ is large enough and the domain of ${\cal A}(x;D_x)$ consists
of a special class of weighted Sobolev function spaces related to conical open
bounded sets of $\rsp^n$, $n \ge 1$.
