{
  "abstract": "This paper is devoted to the shape analysis of the energy of a caloric family of Schauder functions defined on a bounded perforated domain $Ω^o \\setminus \\overline{Ω^i[ϕ]}$ of $\\mathbb{R}^n$, where the outer boundary is fixed, and the inner boundary is obtained by a $C^{1,α}$-perturbation $ϕ$ of the boundary of a reference cavity $Ω^i$. Without imposing any boundary conditions, we prove that in a suitable neighborhood of the identity $ϕ_0$, the domain-to-energy map is of class $C^{\\infty}$. The proof is based on the construction of a global diffeomorphism, smoothly depending on $ϕ$, from the reference annulus onto the perturbed one and on suitable regularity and smoothness assumptions on the pull-back family onto the reference domain. We then apply our main result to two boundary value problems: a nonlinear mixed Robin-type problem and a linear Dirichlet problem. After recalling some known existence and shape analysis results for the solutions, we prove that the corresponding domain-to-energy map is of class $C^{\\infty}$. The proof is based on a decomposition of the fixed domain into near, intermediate, and far regions relative to the cavity, and on the smooth dependence of the layer heat potentials upon support perturbations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.00803",
  "author_total": 2,
  "authors": [
    {
      "name": "Luca Di Persio"
    },
    {
      "name": "Riccardo Molinarolo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fr84y967nka3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.00803",
  "fulltext_url": null,
  "id": "8fr84y967nka3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.00803",
  "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.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.00803",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fr84y967nka3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2607.00803",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.00803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Shape analysis in Schauder spaces of the energy of heat problems in perturbed annular domains",
  "title_text": "Shape analysis in Schauder spaces of the energy of heat problems in perturbed annular domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8fr84y967nka3",
  "venue": "arXiv",
  "versions": []
}