Necessary and sufficient Wiener criterion for the p-parabolic equation

Establish a necessary and sufficient Wiener criterion for boundary regularity of the p-parabolic equation with p ≠ 2 in general space-time domains.

Background

The paper studies boundary regularity for the p-parabolic equation in moving soda-can domains and classifies regularity of the origin in that setting. Wiener-type criteria are known for the Laplace equation and the heat equation, while related capacity estimates have been established for certain cylindrical or otherwise restricted domains.

The authors explicitly identify the absence of a necessary-and-sufficient Wiener criterion in arbitrary space-time domains for the p-parabolic equation when p ≠ 2. Such a criterion would characterize boundary regularity through an appropriate nonlinear parabolic capacity condition beyond the special geometries treated in the existing literature and in this paper.