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Steklov Mathematical Institute Seminar
April 19, 2001, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


Embeddings of Sobolev spaces on a domain with non-regular boundary

O. V. Besov

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Abstract: The embedding theorems obtained by Sobolev for spaces of functions defined on a domain with the cone condition cease to be valid for non-regular domains (for example, for domains having the shape of an external peak in a neighbourhood of certain boundary points).
This report contains embedding and compactness theorems for Sobolev spaces, in terms of geometric properties of the domain. The results encompass also cases involving weighted Sobolev spaces.

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