Open AccessSobolev capacity on the space W1, p(⋅)(ℝn)
Author(s) -
Petteri Harjulehto,
Peter Hästö,
Mika Koskenoja,
S. Varonen
Publication year - 2003
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2003/895261
Subject(s) - sobolev space , mathematics , space (punctuation) , combinatorics , pure mathematics , computer science , operating system
We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[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(⋅)(ℝn)
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