Theory of capacities in fracional Sobolev spaces with variable exponents

Abstract

In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including monotonicity, outer capacity and several results, are studies. We prove that both capacities is a Choquet capacity and all borel sets are capacitable.

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References in corpus (1)

• Trace and extension operators for fractional Sobolev spaces with variable exponent

Cited by in corpus (1)

• Variable exponent Sobolev trace spaces and Dirichlet problem in axiomatic nonlinear potential theory