{
  "abstract": "In this paper, we consider the anisotropic Allen-Cahn equation $-\\operatorname{div} a(Du)+W'(u)=0$ in $\\mathbb{R}^N$, where $a(p):=DH(p)$ with $H(p)=\\frac{1}{2}F(p)^2$ and $F$ a uniformly elliptic integrand, and $W(u)=\\frac{1}{4}(1-u^2)^2$. Based on the Mooney-Yang anisotropic minimal graph, we prove that the anisotropic Allen-Cahn equation admits a stable solution for $N\\geq4$ in the weak sense, whose level sets are not hyperplanes. As a byproduct, we also construct a smooth solution of the above anisotropic Allen-Cahn equation for $N\\geq5$ that is monotone in one direction but is not one-dimensional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30904",
  "author_total": 4,
  "authors": [
    {
      "name": "Haowen Lu"
    },
    {
      "name": "Song Wang"
    },
    {
      "name": "Juncheng Wei"
    },
    {
      "name": "Yuanze Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnxz6k0xe7z49.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30904",
  "fulltext_url": null,
  "id": "bnxz6k0xe7z49",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30904",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7204862522",
  "pdf_url": "https://arxiv.org/pdf/2608.30904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnxz6k0xe7z49.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Entire monotone solutions of the anisotropic Allen-Cahn equation in dimension 5",
  "title_text": "Entire monotone solutions of the anisotropic Allen-Cahn equation in dimension 5",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/bnxz6k0xe7z49",
  "venue": "arXiv",
  "versions": []
}