Geodesic
Imbedding theorems and compactness for spaces of Sobolev type with weights
Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 331-349

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In this article weight estimates are obtained for the intermediate derivatives in spaces of functions which are $p$th power summable together with their gradient of order $l$ over a domain $\Omega$ with respect to a weight which degenerates on the boundary of $\Omega$. In particular, these estimates imply the boundedness and compactness of the corresponding imbeddings. Bibliography: 6 titles. 
@article{SM_1980_36_3_a3,
     author = {P. I. Lizorkin and M. Otelbaev},
     title = {Imbedding theorems and compactness for spaces of {Sobolev} type with weights},
     journal = {Sbornik. Mathematics},
     pages = {331--349},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_3_a3/}
}
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P. I. Lizorkin; M. Otelbaev. Imbedding theorems and compactness for spaces of Sobolev type with weights. Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 331-349. http://geodesic.mathdoc.fr/item/SM_1980_36_3_a3/