Geodesic
Compactness and Inequalities for Partial Derivatives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 194-203

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For various spaces of differentiable functions defined on a domain with a Lipschitz boundary, theorems on the compactness of bounded sets under convergence in a weakened sense are established. 
@article{TM_2005_248_a18,
     author = {S. M. Nikol'skii},
     title = {Compactness and {Inequalities} for {Partial} {Derivatives}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {194--203},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_248_a18/}
}
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S. M. Nikol'skii. Compactness and Inequalities for Partial Derivatives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 194-203. http://geodesic.mathdoc.fr/item/TM_2005_248_a18/