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<p>We consider different notions of capacity related to the parabolic <i>p</i>-Laplace equation. Our focus is on a variational notion, which is consistent in the full range <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10193_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;p&lt;\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. For such a notion we show some basic properties as well as its connection to other notions of capacity presented in the literature, and to a certain parabolic version of the Hausdorff measure. As applications, we use the introduced variational notion of capacity to study polar sets and removability results for supersolutions.</p>

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On notions of p-parabolic capacity and applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月8日

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  • Kristian Moring,
  • Christoph Scheven

摘要

We consider different notions of capacity related to the parabolic p-Laplace equation. Our focus is on a variational notion, which is consistent in the full range \(1<p<\infty \) 1 < p < ∞ . For such a notion we show some basic properties as well as its connection to other notions of capacity presented in the literature, and to a certain parabolic version of the Hausdorff measure. As applications, we use the introduced variational notion of capacity to study polar sets and removability results for supersolutions.