{
  "abstract": "Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we refine the blow up analysis for sequences of solutions of a class of perturbed singular Liouville equations which share the phenomenon of ``blow up and concentration without quantization\". The problem is delicate because we are dealing with the exact threshold value above which one meets the well known ``concentration without quantization\" phenomenon, as recently pushed forward in [C.S. Lin, G. Tarantello, {\\em C. R. Math. Acad. Sci. Paris} (2016)] and in [Y. Lee, C.S. Lin, G. Tarantello, W. Yang, {\\em Comm. PDE.} (2017)]. We overcome these difficulties by developing different strategies for ``fast\" and ``slow\" blow up, combining refined Pohozaev identities, elliptic estimates and ``Sup+CInf\" inequalities in the same spirit of [C.C. Chen, C.S. Lin, {\\em Comm. An. Geom.} (1998)]. In the process, we also derive a new sharp Harnack type inequality by using a moving-plane method, following the ideas in [D. Bartolucci, C.C. Chen, C.S. Lin, G. Tarantello, {\\em Comm. P.D.E.} (2002)].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24346",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniele Bartolucci"
    },
    {
      "name": "Paolo Cosentino"
    },
    {
      "name": "Lina Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhp6p62ktt0ag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24346",
  "fulltext_url": null,
  "id": "dhp6p62ktt0ag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24346",
  "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": "W7171585256",
  "pdf_url": "https://arxiv.org/pdf/2607.24346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhp6p62ktt0ag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2607.24346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Blow up and Concentration without Quantization: sharp Harnack type inequalities",
  "title_text": "Blow up and Concentration without Quantization: sharp Harnack type inequalities",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dhp6p62ktt0ag",
  "venue": "arXiv",
  "versions": []
}