Geodesic
Embedding of Sobolev space in Orlicz space for a~domain with irregular boundary
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 767-778

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In this paper, we establish the embedding of a weighted Sobolev space in an Orlicz space for a domain with irregular boundary. We find an estimate of the order of growth of the $N$-function (defining the Orlicz space) and show that, under certain additional constraints on the weights, this estimate is sharp. We also establish the embedding in the space of continuous functions. 
@article{MZM_2006_79_5_a12,
     author = {Boris V. Trushin},
     title = {Embedding of {Sobolev} space in {Orlicz} space for a~domain with irregular boundary},
     journal = {Matemati\v{c}eskie zametki},
     pages = {767--778},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a12/}
}
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Boris V. Trushin. Embedding of Sobolev space in Orlicz space for a~domain with irregular boundary. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 767-778. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a12/