Embedding of Sobolev space in Orlicz space for a~domain with irregular boundary

Boris V. Trushin

Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 767-778.

Résumé

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.

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