Geodesic
Imbedding theorems for anisotropic Sobolev--Orlicz spaces
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 32-37

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We generalize the Sobolev imbedding theorems to the case of anisotropic Sobolev–Orlich spaces $\mathring{W}^1_{(B)}(\Omega)$. In the case of imbedding of the latter space into the space of all continuous functions we derive an estimate of the continuity module for $u(x)\in\mathring{W}^1_{(B)}(\Omega)$. 
@article{VMUMM_1983_1_a8,
     author = {A. G. Korolev},
     title = {Imbedding theorems for anisotropic {Sobolev--Orlicz} spaces},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {32--37},
     publisher = {mathdoc},
     number = {1},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a8/}
}
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A. G. Korolev. Imbedding theorems for anisotropic Sobolev--Orlicz spaces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (1983), pp. 32-37. http://geodesic.mathdoc.fr/item/VMUMM_1983_1_a8/