{
  "abstract": "We study Robin problems in which a small local boundary coefficient competes with the increasing surface measure of a finite-depth fractal approximation. For a fixed smooth domain, layer potentials give Green function and eigenpair expansions; contour residues and a finite-rank reduction yield a quantitative spectral-gap-dependent eigenvalue remainder. For varying Lipschitz domains, a uniform Poincaré inequality and a trace estimate with respect to normalized surface measure give a uniform ground-state expansion and a rank-one resolvent singularity as the total Robin boundary mass tends to zero. Under the boundary-resolution hypothesis and the condition on the approximation scales, ground-state measurements with known Robin coefficients recover the lower and upper Minkowski dimensions for sequences with bounded total Robin boundary mass. We describe Neumann, generalized Robin, and Dirichlet-type operator limits under the corresponding compact Mosco convergence hypotheses. Koch snowflake computations illustrate the reconstruction formulas, and an exact finite-stage area correction improves the adjacent-stage dimension estimator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34284",
  "author_total": 3,
  "authors": [
    {
      "name": "Habib Ammari"
    },
    {
      "name": "Yat Tin Chow"
    },
    {
      "name": "Fuqun Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ap46857g2gzpf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34284",
  "fulltext_url": null,
  "id": "ap46857g2gzpf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34284",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.34284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ap46857g2gzpf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Recovering fractal boundary dimensions from Robin eigenvalues",
  "title_text": "Recovering fractal boundary dimensions from Robin eigenvalues",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ap46857g2gzpf",
  "venue": "arXiv",
  "versions": []
}