{
  "abstract": "We consider a two-well problem within geometrically linear elasticity, on a bounded Lipschitz set in dimension $n\\ge 2$. We assume that the two wells are compatible through a symmetrized rank-one connection and that the displacement matches their average on the boundary, and we include a regularization based on the total surface energy. We show that there are two distinct regimes, with the energy scaling differently in terms of the surface-energy coefficient $\\eps$: it is proportional to $\\eps^{2/3}$ if there are two distinct compatible twin-normal directions, and to $\\eps^{4/5}$ if there is only one. This matches previous findings in rectangles and other special geometries, mostly in two dimensions, and the lower bounds obtained by a Fourier method by Raiţă, Rüland, Tissot and Tribuzio (2024). Our results are obtained by explicit constructions, which contain a self-similar refinement of oscillations close to the boundary, and by a short real-space proof of the matching lower bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04329",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergio Conti"
    },
    {
      "name": "Oleksandr Misiats"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1by7z335m76a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04329",
  "fulltext_url": null,
  "id": "f1by7z335m76a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04329",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1by7z335m76a.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04329"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Scaling laws for linear-elastic two-variant martensitic phase transitions in general domains",
  "title_text": "Scaling laws for linear-elastic two-variant martensitic phase transitions in general domains",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/f1by7z335m76a",
  "venue": "arXiv",
  "versions": []
}