{
  "abstract": "We consider the Hardy inequality associated with a strongly convex Finsler norm $F$ on $\\mathbb{R}^n$ and we study its optimal non-homogeneous improvements in the whole range $1<p<\\infty$. We show that the anisotropic Hardy difference controls a weighted critical Sobolev norm when $1<p<n$, a weighted exponential integrability of Trudinger type when $p=n$, where the Hardy term is replaced by its Leray logarithmic correction, and a weighted Hölder seminorm when $p>n$, proving in each regime that the logarithmic weights appear with the optimal exponents. In the borderline case $p=n$ this extends to general functions the optimal exponent previously known only for anisotropically radial functions. The proofs rely on a common ground-state reduction, combined with a splitting into an $F_o$-radial and a mean-free part for $1<p\\le n$, and with an anisotropic Morrey representation formula for $p>n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33346",
  "author_total": 3,
  "authors": [
    {
      "name": "Giuseppina di Blasio"
    },
    {
      "name": "Giovanni Pisante"
    },
    {
      "name": "Georgios Psaradakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/186pr3v4e3b5s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33346",
  "fulltext_url": null,
  "id": "186pr3v4e3b5s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33346",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223806270",
  "pdf_url": "https://arxiv.org/pdf/2610.33346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/186pr3v4e3b5s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Optimal Non-Homogeneous Improvements of the Anisotropic Hardy Inequality",
  "title_text": "Optimal Non-Homogeneous Improvements of the Anisotropic Hardy Inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/186pr3v4e3b5s",
  "venue": "arXiv",
  "versions": []
}