{
  "abstract": "Let $N\\ge 2$ and $1<p<N$. Let $H$ be a possibly non-reversible Minkowski norm on $\\mathbb{R}^N$, with $H\\in C^2(\\mathbb{R}^N\\setminus\\{0\\})$ and $D^2(H^2/2)$ uniformly positive definite away from the origin. We classify all nonnegative local weak solutions $u\\in W^{1,p}_{\\rm loc}(\\mathbb{R}^N)$ of \\[ -\\operatorname{div}\\big(H(\\nabla u)^{p-1}\\nabla H(\\nabla u)\\big)=u^{p^*-1},\\qquad p^*=\\frac{Np}{N-p}, \\] without any finite-energy, integrability, or asymptotic assumption. Every nonzero solution is an anisotropic Sobolev bubble. This settles, for the full range $1<p<N$, the anisotropic analogue of Problem A of Antonini--Ciraolo--Gatti, whose Euclidean case was settled by Zhang, and removes the restriction on $p$ in the non-energy anisotropic classification of Chen--Wu--Yan--Yang. We also prove a scale-invariant Schoen-type Harnack inequality for local solutions. The proof follows the strategy of Zhang for the Euclidean $p$-Laplacian, combining rigidity of bounded blow-up profiles and a first-contact argument with the integral bootstrap of Ciraolo and Gatti. The anisotropic analysis requires two additional ingredients. First, we establish a Bochner identity for the conjugated stress tensor in distributional form on the noncritical set, using only $C^2$ regularity of $H$. Second, we prove a two-term expansion at isolated singularities of Finsler $p$-harmonic functions, including the gradient control needed by the Pohozaev invariant. For non-reversible anisotropies the argument is formulated with the reflected norm. A Morrey-type estimate proved directly for the relevant Leray--Lions operator replaces the potential-theoretic input used in the Euclidean argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00337",
  "author_total": 1,
  "authors": [
    {
      "name": "Phuong Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/995r3e286qayt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00337",
  "fulltext_url": null,
  "id": "995r3e286qayt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00337",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7216206730",
  "pdf_url": "https://arxiv.org/pdf/2610.00337",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/995r3e286qayt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00337",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00337"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Critical anisotropic $p$-Laplace equations without finite energy: classification and a Schoen-type Harnack inequality",
  "title_text": "Critical anisotropic p-Laplace equations without finite energy: classification and a Schoen-type Harnack inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/995r3e286qayt",
  "venue": "arXiv",
  "versions": []
}