Sobolev capacity on the space W1, p(⋅)(ℝn)

By Petteri Harjulehto, P. Hasto, M. Koskenoja, Susanna Varonen. 2003

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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).

Subfields: Applied Mathematics

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