Differentiability points of functions in weighted Sobolev spaces

We consider weighted Sobolev spaces $W_p^l$, $l\in\mathbb N$, with weighted $L_p$-norm of higher derivatives on an $n$-dimensional cube-type domain. The weight $\gamma$ depends on the distance to an $(n-d)$-dimensional face $E$ of the cube. We establish the property of uniform $L_p$-differentiability of functions in these spaces on the face $E$ of an appropriate dimension. This property consists in the possibility of $L_p$-approximation of the values of a function near $E$ by a polynomial of degree $l-1$.