{
  "abstract": "We classify isolated singularities of nonnegative weak solutions to the Serrin-critical quasilinear Lane-Emden equation $-Δ_p u=u^{\\frac{n(p-1)}{n-p}}$ in $B_1\\setminus\\{0\\}$, where $1<p<n$, $Δ_p$ is the classical $p$-Laplacian operator and $B_1\\setminus\\{0\\}\\subset\\mathbb{R}^n$ is the punctured unit ball. We prove that either the origin is a removable singularity or $u$ satisfies $\\lim_{x\\to0}|x|^{\\frac{n-p}{p-1}}(\\log\\frac1{|x|})^{\\frac{n-p}{p(p-1)}}u(x)=[\\frac{n-p}{p}(\\frac{n-p}{p-1})^{p-1}]^{\\frac{n-p}{p(p-1)}}$. This extends the result of Aviles (Comm. Math. Phys. 1987: 177--192) from the semilinear case $p=2$ to the full range $1<p<n$, without assuming radial symmetry. We develop a new BV-based argument for weak solutions. We also give a direct construction of positive radial singular solutions with the same asymptotic behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23045",
  "author_total": 2,
  "authors": [
    {
      "name": "Meiqing Xu"
    },
    {
      "name": "Hui Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cx7xaa3h87wct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23045",
  "fulltext_url": null,
  "id": "cx7xaa3h87wct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23045",
  "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": "W7222926443",
  "pdf_url": "https://arxiv.org/pdf/2610.23045",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cx7xaa3h87wct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23045",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23045"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isolated singularities of weak solutions to the Serrin-critical $p$-Laplace equation",
  "title_text": "Isolated singularities of weak solutions to the Serrin-critical p-Laplace equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/cx7xaa3h87wct",
  "venue": "arXiv",
  "versions": []
}