Geodesic
Differentiability points of functions in weighted Sobolev spaces
Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 257-266

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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 $l-1$. 
@article{TRSPY_2013_283_a16,
     author = {A. I. Tyulenev},
     title = {Differentiability points of functions in weighted {Sobolev} spaces},
     journal = {Informatics and Automation},
     pages = {257--266},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a16/}
}
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A. I. Tyulenev. Differentiability points of functions in weighted Sobolev spaces. Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 257-266. http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a16/