{
  "abstract": "We study normalized solutions to the 1-Laplace equation \\[ -\\mbox{div}\\left(\\frac{Du}{|Du|}\\right)+λ\\frac{u}{|u|}=f(u)+|u|^{1^*-2}u,\\quad\\mbox{in}~ \\mathbb{R}^N \\] subject to the constraint $\\int_{\\mathbb{R}^N}|u| \\, \\mbox{d}x=m$, where $N\\geq2$, $1^*=\\frac{N}{N-1}$ is the critical Sobolev exponent for the embedding from BV into $L^p$, $λ, m\\in\\mathbb{R}^+$ and $f:\\mathbb{R}\\to\\mathbb{R}$ is a continuous nonlinear perturbation. We first establish a Pohozaev-type identity for the equation and use it to study the associated critical energy, and then prove the existence of normalized solutions via nonsmooth critical point theory. A key feature of our approach is the proof of the existence of a Palais-Smale sequence for a Lipschitz continuous functional under a Lipschitz continuous constraint. This is significantly different in methodology from previous problems with $C^2$ constraint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12224",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhouxin Li"
    },
    {
      "name": "Ruishu Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1sb3vp3e5e5fd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12224",
  "fulltext_url": null,
  "id": "1sb3vp3e5e5fd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12224",
  "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": "W7221183061",
  "pdf_url": "https://arxiv.org/pdf/2610.12224",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1sb3vp3e5e5fd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12224",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12224"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Normalized solutions to 1-Laplace equations with critical growth term",
  "title_text": "Normalized solutions to 1-Laplace equations with critical growth term",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/1sb3vp3e5e5fd",
  "venue": "arXiv",
  "versions": []
}