Capacity Estimates, Differentiation Bases and Quasisuperminimizers in Orlicz-Sobolev Spaces on Metric Measure Spaces

Based on the capacity instead of measure, we characterize Orlicz-Sobolev capacity and variational Orlicz-Sobolev capacity in Orlicz-Sobolev spaces on metric measure spaces. Meanwhile, we also obtain the equivalent results about the differentiation bases and quasisuperminimizers for the convex integral functional.