{
  "abstract": "We study stable regular solutions of the variable-coefficient equation $-\\operatorname{div}((A(x)\\nabla u\\cdot\\nabla u)^{p/2-1}A(x)\\nabla u)=f(u)$ in $B_1\\subset\\mathbb{R}^n$, where $p>1$, $f\\in C^1(\\mathbb{R})$ is nonnegative, and $A$ is a locally Lipschitz, symmetric, uniformly elliptic matrix field. We prove quantitative interior Hölder estimates for $n<p+4p/(p-1)$ when $p\\ge2$, and for $n<5p$ when $1<p<2$. We also obtain interior energy estimates and higher integrability of the gradient in every dimension. These estimates are given in terms of $\\|u\\|_{L^1(B_1)}$, with constants depending only on $n,p$, the ellipticity bounds, and a local $L^\\infty$ bound for $DA$, but not on $f$ or higher derivatives of $A$. These results extend the corresponding interior estimates of Cabré, Miraglio, and Sanchón for the $p$-Laplace equation to this variable-coefficient setting. The proof uses weighted Hessian estimates to control coefficient errors and a comparison between radial and full gradient energies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00730",
  "author_total": 1,
  "authors": [
    {
      "name": "Weican Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/416zf418ya7gn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00730",
  "fulltext_url": null,
  "id": "416zf418ya7gn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00730",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/416zf418ya7gn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stable solutions to $p$-Laplacian type equations with variable coefficients",
  "title_text": "Stable solutions to p-Laplacian type equations with variable coefficients",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/416zf418ya7gn",
  "venue": "arXiv",
  "versions": []
}