{
  "abstract": "Inspired by questions related to inverse problems and shape optimization, we derive an asymptotic expansion of the voltage potential, solution to a model elliptic second-order partial differential equation, under small perturbations of its boundary conditions. More precisely, the homogeneous Dirichlet or homogeneous Neumann boundary condition in a fixed, reference configuration of the problem is replaced by a Robin boundary condition with admittance $k_\\varepsilon > 0$ on a ``small'' subset $ω_\\varepsilon$ of the boundary of the ambient domain, vanishing at the limit $\\varepsilon \\to 0$. In each of these two situations, a general asymptotic formula is established for the voltage potential, which rests on minimal assumptions about the shape of the vanishing subset $ω_\\varepsilon$ and the parameter $k_\\varepsilon$. The scalings of these expansions, capturing the intensity of the perturbation, are measured by new quantities called ``Robin-Dirichlet'' capacity or a ``Robin-Neumann'' capacity, which depend on the geometry of $ω_\\varepsilon$ and on the value of the parameter $k_\\varepsilon$. We analyze how these quantities compare to more classical measures of the ``smallness'' of $ω_\\varepsilon$, such as the capacity or the Neumann capacity of $ω_\\varepsilon$, according to the behavior of $k_\\varepsilon$ as $\\varepsilon \\to 0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05283",
  "author_total": 3,
  "authors": [
    {
      "name": "Eric Bonnetier"
    },
    {
      "name": "Charles Dapogny"
    },
    {
      "name": "Roman Moskalenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5cxdz8wrpm49a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05283",
  "fulltext_url": null,
  "id": "5cxdz8wrpm49a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05283",
  "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",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7211910795",
  "pdf_url": "https://arxiv.org/pdf/2609.05283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5cxdz8wrpm49a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic expansion of the voltage potential under small Robin perturbations of its boundary conditions",
  "title_text": "Asymptotic expansion of the voltage potential under small Robin perturbations of its boundary conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/5cxdz8wrpm49a",
  "venue": "arXiv",
  "versions": []
}