Fractional capacities relative to bounded open Lipschitz sets complemented

摘要

As a complement of (Shi and Xiao in PotentialAnal 45: 261-298, 2016) this article addresses five more aspects of the fractional capacities relative to bounded open Lipschitz subsets of R-n: (i) quasi-everywhere version; (ii) unique extremal; (iii) energy functional; (iv) dual representation; (v) fine behaviour of each fractional Sobolev function in R-n.