A direct approach to Orlicz–Sobolev capacity Original Research Article

This paper is motivated by Federer and Ziemerʹs potential-free approach to Sobolev capacity. We extend their results to Orlicz–Sobolev spaces and analyze the resulting notion of Orlicz–Sobolev capacity. In particular, we explore the relationship between the Orlicz–Sobolev capacity of a set and its Hausdorff dimension and then establish the quasicontinuity of Orlicz–Sobolev functions.