English

On notions of $p$-parabolic capacity and applications

Analysis of PDEs 2024-09-25 v1

Abstract

We consider different notions of capacity related to the parabolic pp-Laplace equation. Our focus is on a variational notion, which is consistent in the full range 1<p<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.

Keywords

Cite

@article{arxiv.2409.16066,
  title  = {On notions of $p$-parabolic capacity and applications},
  author = {Kristian Moring and Christoph Scheven},
  journal= {arXiv preprint arXiv:2409.16066},
  year   = {2024}
}