{
  "abstract": "This work is devoted to the study of blow-up phenomena for solutions of \\[-Δu=λV(x)|x|^{2N}e^v,\\quad \\mbox{in}\\quad B_1,\\quad v=0\\quad \\mbox{on}\\quad \\partial B_1. \\] where $B_1$ denotes the unit ball in $\\mathbb R^2$ centered at the origin, $V(x)$ is a positive smooth function, $N\\in \\mathbb N$ and $λ>0$ is a small parameter. The main goal is to determine conditions on the potential $V$ guaranteeing the existence of families of solutions that blow up at the origin as $λ\\to 0^+$. Moreover, we establish higher order criteria that distinguish between simple and non-simple blow-up behavior at $x=0$. In particular, for $N-1\\in 2^{\\mathbb N}$, we construct a non-simple blow-up sequence $v_k$, corresponding to coefficient function $V_k$ whose derivatives vanish up to the maximal order allowed by the upper bound of Wei-Zhang, thereby proving that this bound is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10968",
  "author_total": 3,
  "authors": [
    {
      "name": "Teresa D'Aprile"
    },
    {
      "name": "Juncheng Wei"
    },
    {
      "name": "Lei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2x8h3hdasdn2s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10968",
  "fulltext_url": null,
  "id": "2x8h3hdasdn2s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10968",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221093649",
  "pdf_url": "https://arxiv.org/pdf/2610.10968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2x8h3hdasdn2s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Higher-order criteria and sharpness for blow-up at quantized singularities in Liouville equations",
  "title_text": "Higher-order criteria and sharpness for blow-up at quantized singularities in Liouville equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/2x8h3hdasdn2s",
  "venue": "arXiv",
  "versions": []
}