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Journal of Function Spaces and Applications
Volume 1 (2003), Issue 1, Pages 17-33
http://dx.doi.org/10.1155/2003/895261

Sobolev capacity on the space W1,p()(n)

Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland

Received 1 December 2002

Academic Editor: Vladimir Maz'ya

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define Sobolev capacity on the generalized Sobolev space W1,p()(n). It is a Choquet capacity provided that the variable exponent p:n[1,) is bounded away from 1 and . We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the space W1,p()(n).