Theory of capacities in fracional Sobolev spaces with variable exponents

2019/04/18 by Baalal, Azeddine, Berghout, Mohamed
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1904.08997

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.

Related

• The variable exponent BV-Sobolev capacity
• Fractional variable exponents Sobolev trace spaces
• Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents
• Some Properties of Thinness and Fine Topology with Relative Capacity
• Strauss and Lions type theorems for the fractional Sobolev spaces with\n variable exponent and applications to nonlocal Kirchhoff-Choquard problem