{
  "abstract": "In this paper we prove a quantization property for Palais-Smale sequences of functionals related to Liouville equations on compact surfaces. While these equations have been extensively studied over the past decades, such a quantization property had not been established so far, and has been often bypassed by the Struwe monotonicity trick. Our result, which relies on careful $L^p$ estimates to obtain gradient bounds and to perform neck analysis, allows to directly apply variational methods to obtain existence of solutions in non-resonant regimes. We also give an example of clustering of blow-up points and a stronger assumption that, on the contrary, guarantees that the blow-up points are isolated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21851",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrea Malchiodi"
    },
    {
      "name": "Francesco Malizia"
    },
    {
      "name": "Luca Martinazzi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dadq5arc6hvqg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21851",
  "fulltext_url": null,
  "id": "dadq5arc6hvqg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21851",
  "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": "W7213942220",
  "pdf_url": "https://arxiv.org/pdf/2609.21851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dadq5arc6hvqg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantization for Palais-Smale sequences of the Liouville functional on closed surfaces",
  "title_text": "Quantization for Palais-Smale sequences of the Liouville functional on closed surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/dadq5arc6hvqg",
  "venue": "arXiv",
  "versions": []
}