{
  "abstract": "We show that scalar local minimizers of the Allen-Cahn functional with the double-well potential and homogeneous Neumann boundary conditions on a bounded Lipschitz domain are isolated in the $L^1$-topology. This affirmatively answers a question raised by Kohn and Sternberg (Local minimisers and singular perturbations, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989)). The proof implements an analytic Lyapunov-Schmidt reduction inspired by the theory of monotone dynamical systems in works of Jiang-Yu and Hirsch-Smith in an elliptic setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11797",
  "author_total": 1,
  "authors": [
    {
      "name": "Nam Q. Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ec411seqeeayk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11797",
  "fulltext_url": null,
  "id": "ec411seqeeayk",
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  "landing_url": "https://arxiv.org/abs/2609.11797",
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  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
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    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212293066",
  "pdf_url": "https://arxiv.org/pdf/2609.11797",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ec411seqeeayk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.11797",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11797"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isolation of scalar Allen-Cahn local minimizers",
  "title_text": "Isolation of scalar Allen-Cahn local minimizers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ec411seqeeayk",
  "venue": "arXiv",
  "versions": []
}