Generation type inequalities for closed linear operators related to domains with conical points

Abstract

Let ${\cal A}(x;D_x)$ be a second-order linear differential operator in divergence form. We prove that the operator $łI- {\cal A}(x;D_x)$, where $ł\in\csp$ and $I$ stands for the identity operator, is closed and injective when ${\rm Re}ł$ 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 $\rsp^n$, $n \ge 1$.