Abstract. Continuous and compact imbeddings of weighted Sobolev spaces $W^{1,p}(\Omega; v)$ and $W_0^{1,p}(\Omega; v)$ into the weighted Lebesgue space $L^q (\Omega; w)$, where $1\le q< p< \infty $, have been considered, where the weights $v$ and $w$ are some functions of the distance measured either from the boundary $\partial\Omega $ of $\Omega $ or from a point $x_0 \in\partial \Omega $ and $\Omega $ is a bounded domain of ${{\msbm R}^N}$ in the class ${{\cal C}^{0,1}}$, ${{\cal K}(x_0), {\cal K}^{0,1}(x_0)}$.

AMS Subject Classification (1991): 46E35

Received October 26, 1998, and in final form September 15, 1999. (Registered under 2759/2009.)