This article is cited in 11 papers

Sobolev Embedding Theorems for a Class of Anisotropic Irregular Domains

Boris V. Trushin

Moscow Institute of Physics and Technology

Abstract: Sufficient conditions for the embedding of a Sobolev space in Lebesgue spaces on a domain depend on the integrability and smoothness parameters of the spaces and on the geometric features of the domain. In the present paper, Sobolev embedding theorems are obtained for a class of domains with irregular boundary; this class includes the well-known classes of $\sigma$-John domains, domains with the flexible cone condition, and their anisotropic analogs.

UDC: 517.518.23

Received in May 2007

 English version: Proceedings of the Steklov Institute of Mathematics, 2008, 260, 287–309

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