{
  "abstract": "For every $p>1$, we prove that a nontrivial solution of \\begin{equation*} -Δ_pu=f(x,u,\\nabla u) \\end{equation*} in a planar domain, with $|f(x,s,ξ)|\\leq C(|s|^{p-1}+|ξ|^{p-1})$, vanishes neither on an open set nor to infinite order at a point. This allows us to prove unique continuation properties of axially symmetric solutions to $p$-Laplace equations in higher dimensions $N\\geq3$, with axially symmetric $p$-harmonic functions as a particular case. Unlike in our previous work, the analysis is based here on the regularity and quasiconformal properties of the whole stress field $|\\nabla u|^{p-2}\\nabla u$ in the plane, taking into account the more delicate regularity theory for $p>2$. This allows us to prove Liouville-type and bubble profile decomposition results for critical problems in dimensions $N\\geq3$ and in the whole range $1<p<N$, under some symmetry conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06694",
  "author_total": 1,
  "authors": [
    {
      "name": "Carlo Mercuri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0tr4c5zbxxwcg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06694",
  "fulltext_url": null,
  "id": "0tr4c5zbxxwcg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06694",
  "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/2611.06694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0tr4c5zbxxwcg.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unique continuation, nonexistence and bubbling for the critical $p$-Laplace equation II: the degenerate elliptic case and higher dimensions",
  "title_text": "Unique continuation, nonexistence and bubbling for the critical p-Laplace equation II: the degenerate elliptic case and higher dimensions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/0tr4c5zbxxwcg",
  "venue": "arXiv",
  "versions": []
}