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

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

2006-07-14

arxiv.org/abs/math/0607341v1

Appl. Anal. 84 (2005), no. 3, 283--310

Mathematics

Analysis of PDEs

Scientific paper

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 $\rsp^n$, $n \ge 1$.

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