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arXiv · 2409.16066

On notions of $p$-parabolic capacity and applications

Kristian Moring·Christoph Scheven
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Abstract

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 $1<p<\infty$. 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.

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Kristian Moring, Christoph Scheven. 2024-09-24. On notions of $p$-parabolic capacity and applications. https://arxiv.org/abs/2409.16066

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