{
  "abstract": "We consider the time-harmonic Maxwell's equations in a closed, cylindrical waveguide with longitudinal invariant but heterogeneous permittivity and permeability. We consider minimal smoothness assumptions, i.e., the material parameters have to be in $L^\\infty$ and the cross section has to be Lipschitz with a possibly non-trivial topology. First, we show that the associated Calderón operator is well-defined and bounded in the natural trace spaces $\\mathbf{H}_0^{-1/2}(\\operatorname{curl}_Γ;Γ) \\to \\mathbf{H}_0^{-1/2}(\\operatorname{div}_Γ;Γ)$. Second, we consider interior Maxwell problems obtained from using the Calderón operator and analyze their well-posedness. Furthermore, we report some additional results on the location and group velocities of the waveguide wavenumbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21855",
  "author_total": 1,
  "authors": [
    {
      "name": "Martin Halla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh3t2tc8eshpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21855",
  "fulltext_url": null,
  "id": "dh3t2tc8eshpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21855",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.21855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh3t2tc8eshpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Calderón operator for time-harmonic Maxwell's equations in closed waveguides",
  "title_text": "The Calderón operator for time-harmonic Maxwell's equations in closed waveguides",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/dh3t2tc8eshpr",
  "venue": "arXiv",
  "versions": []
}