Imbedding theorems for spaces of functions with partial derivatives that are summable in various powers

We consider the anisotropic spaces $W_{\bar p}^{\bar l}(\Omega)$, $\bar l=(l_1,l_2,\dots,l_n)$, $l_i>0$, $\bar p=(p_1,p_2,\dots$, $1<p_i<\infty$, $i=1,2,\dots n$. We extend the class of domains for which imbedding theorems for these spaces have the same form as for $E_n$. We investigate complete continuity of the corresponding imbedding operators.