{
  "abstract": "We classify the regularity of the origin for the $p$-parabolic equation in the soda-can domains $$Θ_{l,θ}=\\{(x,t)\\in\\mathbb{R}^n\\times\\mathbb{R}:0 < -t < θ|x|^l < θ\\},\\text{ where }l,θ>0.$$ The classification covers every $p>1$ in dimensions $n\\ge2$. At the endpoint $l=p$, the origin is regular if and only if $p\\ge2n/(n+1)$. We also prove that the origin admits a traditional barrier for every $p>2$ and $l>0$. When $2 < p < n$ and $l < p$, the origin is nevertheless irregular. This answers negatively the well-known open question whether one barrier suffices to characterize boundary regularity in the degenerate range $p>2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06497",
  "author_total": 2,
  "authors": [
    {
      "name": "Benny Avelin"
    },
    {
      "name": "Mikko Parviainen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g3gnfyams1k2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06497",
  "fulltext_url": null,
  "id": "3g3gnfyams1k2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06497",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220667535",
  "pdf_url": "https://arxiv.org/pdf/2610.06497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3g3gnfyams1k2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity of soda-can domains for the $p$-parabolic equation",
  "title_text": "Regularity of soda-can domains for the p-parabolic equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3g3gnfyams1k2",
  "venue": "arXiv",
  "versions": []
}