Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

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 $h(\cdot).$

Publication Details

Journal
ArXiv.org
Published
2025-03-17
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

ArXiv.org
Nonlinear Partial Differential Equations
article

Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces

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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 $h(\cdot).$

ArXiv.org
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Nonlinear Partial Differential Equations
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Capacity and Hausdorff measure in Musielak-Orlicz-Sobolev spaces · ArXiv.org (2025) | TGRS Research Map | TGRS