Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

Abstract

In this paper, we show that sets with zero Sobolev $p(\cdot )$-capacity have generalized Hausdorff $h(\cdot )$-measure zero, for some gauge function $h(\cdot ).$ We also prove that sets with zero Musielak-Orlicz-Sobolev $\Phi (\cdot ,\cdot )$-capacity, for a particular class of functions $\Phi (\cdot ,\cdot ),$ have generalized Hausdorff $h(\cdot )$-measure zero, for a suitable gauge function $h(\cdot ).$

15 pages