Abstract We define Sobolev capacity on the generalized Sobolev space W1,p(·)(Rn). It is a Choquet capacity provided that the variable exponent p : R^n -> [1, \infty) is bounded away from 1 and infinity. 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).
2000 Mathematics Subject Classification: Primary 46E35; Secondary 31B15
Keywords: Sobolev capacity, variable exponent, generalized Sobolev space,
Hausdorff dimension, quasicontinuous representative.
Go to J. Funct. Spaces Appl.
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See also:
Variable exponent Lebesgue and Sobolev spaces research group
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