On notions of $p$-parabolic capacity and applications

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.