{
  "abstract": "We study Moser–Trudinger inequalities with singular weights and nonlinear perturbations for zero-mean functions on a smooth bounded domain Ω⊂R2 with 0∈∂Ω. We consider supu∈H1(Ω), ∥∇u∥22=1∫Ωudx=0∫Ωe2π(1−β)u2q(∥u∥22)|x|2βdx, where 0<β<1 and q(t)=1+a1t+⋯+aktk has nonnegative coefficients. Under the cascading conditions 0≤a1<λ and 0≤aj≤λaj−1 (j=2,…,k), where λ is the first nonzero Neumann eigenvalue, we prove that the supremum is finite. Our results unify and extend the improved Moser–Trudinger inequality of Lu–Yang for zero-mean functions and the singular Moser–Trudinger inequality of Zhu.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741000, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Geijuan Gong",
      "orcid": "0009-0001-4887-9128"
    },
    {
      "affs": [
        0
      ],
      "name": "Yueli Liu"
    },
    {
      "affs": [
        0
      ],
      "name": "Xin Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqfsyj6zx9n1k.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214106",
  "fulltext_url": null,
  "id": "fqfsyj6zx9n1k",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4106",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/fqfsyj6zx9n1k.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T00:21:18Z",
      "native_id": "10.3390/math14214106",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Improved Moser–Trudinger Inequalities with Singular Weights and Nonlinear Perturbations for Zero-Mean Functions",
  "title_text": "Improved Moser–Trudinger Inequalities with Singular Weights and Nonlinear Perturbations for Zero-Mean Functions",
  "type": "peer-reviewed",
  "updated_at": "2026-11-10T00:21:18Z",
  "url": "https://research.draconitic.com/paper/fqfsyj6zx9n1k",
  "venue": "Mathematics",
  "versions": []
}