Year: 2026
Type: preprint
Abstract: We characterize boundary regularity for $u_t=Δ_p u$ in arbitrary bounded open subsets of $\mathbb{R}^{n+1}$ for $n\ge2$ and $p\in(2n/(n+1),2)\cup (2,\infty)$. We prove equivalent Wiener criteria in terms of capacitary potentials on prescribed cylinders and in terms of intrinsic capacities. Both require divergence at every positive obstacle height. Independently, we prove Perron resolutivity for continuous data on the full topological boundary of every nonempty bounded open set for all $n\geq 1$ and $p>1$. As an application of the Wiener criterion, we prove a Petrovski\uı-type criterion in the singular range, which gives regularity of the origin for $|x|0$. For $2
Source: arXiv (Cornell University)
Authors: Avelin, Benny, Parviainen, Mikko
Institutions: Uppsala University, University of Jyväskylä
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223051813