{
  "abstract": "In this paper, we prove global pointwise estimates on the decreasing rearrangement \\(u^{\\ast}\\) and \\([H(\\nabla u)]^{\\ast}\\) of SOLAs \\(u\\) of an elliptic Poisson equation driven by the anisotropic \\(p\\)-Laplace operator \\(Δ_p^H\\) for given \\(L^1\\)-data and equipped with either homogeneous Dirichlet or Neumann boundary conditions. Here, we assume that the dimension \\(n\\ge 2\\), \\(1<p<n\\) and \\(H\\) is norm on \\(\\R^n\\). In the degenerate range \\(2 \\leq p <n\\), this gives an anisotropic extension and a full-interval completion of the rearrangement theory of Cianchi-Maz'ya [JEMS, 2014]. In particular, we obtain a new rearrangement estimate for gradients by decomposing the data for singular range \\(1<p<2\\), where the nonlinear interpolation method aren't available. Moreover, the endpoint weak-type gradient estimate is obtained for all \\(1<p<n\\). In the range \\(p_*(n)<p<n\\) with \\(p_*(n):=\\frac{3n-2}{2n-1}\\), we prove a stability estimate for differences of gradients. These results extends the known ones in the literature to the singular range \\(p_*(n)<p<2\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13226",
  "author_total": 3,
  "authors": [
    {
      "name": "Lu Chen"
    },
    {
      "name": "Daniel Hauer"
    },
    {
      "name": "Yabo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5k4d1maa1s3gj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13226",
  "fulltext_url": null,
  "id": "5k4d1maa1s3gj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13226",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221549933",
  "pdf_url": "https://arxiv.org/pdf/2610.13226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5k4d1maa1s3gj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gradient rearrangement estimates for singular and degenerate anisotropic $p$-Laplace equations",
  "title_text": "Gradient rearrangement estimates for singular and degenerate anisotropic p-Laplace equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/5k4d1maa1s3gj",
  "venue": "arXiv",
  "versions": []
}