Characterizations of interior polar sets for the degenerate p-parabolic equation

TL;DR

This paper explores the properties of interior polar sets related to the degenerate p-parabolic equation, establishing their characterization via nonlinear capacity, removability for supersolutions, and connection to parabolic Hausdorff measure.

Contribution

It provides new characterizations of sets with zero nonlinear parabolic capacity and links these to removability and measure-theoretic properties for the p-parabolic equation.

Findings

Interior polar sets characterized by zero nonlinear capacity

Zero capacity sets are removable for bounded supersolutions

Zero capacity sets relate to parabolic Hausdorff measure

Abstract

This paper deals with different characterizations of sets of nonlinear parabolic capacity zero, with respect to the parabolic p-Laplace equation. Specifically we prove that certain interior polar sets can be characterized by sets of zero nonlinear parabolic capacity. Furthermore we prove that zero capacity sets are removable for bounded supersolutions and that sets of zero capacity have a relation to a certain parabolic Hausdorff measure.