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arXiv · 2503.12849

Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

Ankur Pandey·Nijjwal Karak·Debarati Mondal
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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 $h(\cdot).$

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Ankur Pandey, Nijjwal Karak, Debarati Mondal. 2025-03-17. Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces. https://arxiv.org/abs/2503.12849

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