THEORY OF CAPACITIES IN FRACTIONAL SOBOLEV SPACES WITH VARIABLE EXPONENTS
Résumé
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. Mathematics Subject Classification: Primary 31B15, 46E35.
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