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arXiv · 1904.08997

Theory of capacities in fracional Sobolev spaces with variable exponents

Azeddine Baalal·Mohamed Berghout
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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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Azeddine Baalal, Mohamed Berghout. 2019-04-18. Theory of capacities in fracional Sobolev spaces with variable exponents. https://arxiv.org/abs/1904.08997

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