{
  "abstract": "We develop a general principle for passing from the analysis of partial differential operators on the whole space to boundary value problems on the half-space. The reduction separates the boundary problem into restricted invertibility of the interior operator and a complementing problem formulated entirely on the trace space. For a broad class of operators admitting suitable factorizations, the restricted invertibility is governed by the whole-space theory of the factors, while the complementing problem determines both well-posedness and the admissible combinations of interior and boundary data. In this way, boundary value theory is reduced to whole-space operator theory together with an explicit analysis on the trace space. We realize this principle for time-periodic partial differential equations and systems of mixed order, developing the required Newton-polygon function spaces, interpolation theory, and $L^p$-trace theory. For mixed-order differential operators under general boundary conditions, well-posedness and the admissible data space are determined by an explicit complemented boundary matrix. This yields new $L^p$-well-posedness results for Cahn--Hilliard equations with dynamic boundary conditions and for Cahn--Hilliard--Gurtin systems. Most notably, we obtain the first maximal $L^p$-regularity result for a genuinely mixed-order interior system coupled to dynamic boundary conditions carrying a distinct mixed-order structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.12250",
  "author_total": 2,
  "authors": [
    {
      "name": "Guillaume Neuttiens"
    },
    {
      "name": "Jonas Sauer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5capbvr2sacb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.12250",
  "fulltext_url": null,
  "id": "5capbvr2sacb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.12250",
  "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"
    ],
    [
      "openalex",
      "2604|Differential Equations and Boundary Problems"
    ]
  ],
  "openalex": "W7202396335",
  "pdf_url": "https://arxiv.org/pdf/2608.12250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5capbvr2sacb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2608.12250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.12250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "From Whole-Space Theory to Boundary Value Problems for Mixed-Order PDEs",
  "title_text": "From Whole-Space Theory to Boundary Value Problems for Mixed-Order PDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5capbvr2sacb4",
  "venue": "arXiv",
  "versions": []
}