This article is cited in 6 papers

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

Boris V. Trushin

Moscow Institute of Physics and Technology

Abstract: 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.

UDC: 517.518.232

Received: 16.05.2002

DOI: 10.4213/mzm2748

 English version: Mathematical Notes, 2006, 79:5, 707–718

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