{
  "abstract": "In the context of locally convex vector valued integrable tensors on open sets of a $n$-dimensional manifold $M$ developped in our previous work \\cite{sil09261621}, in this paper we construct a framework in which to address both a variational problem associated with a Lagrangian $\\mathscr{L}$, and a conservation law on-shell associated with actions $ϕ$ and $ω$. $\\mathscr{L}$ is a $C^{p}$-map valued in a quasi-complete Hausdorff lcs $\\mathcal{Z}$ and defined on an open set $O$ of a normed space, $ϕ$ is a $C^{p}$-action parametrized by an open $A$ of a normed space $T$, acting over the space $\\mathfrak{Z}^{O}$ of fields valued in a normed space $Y_{0}$ and defined on $W$ domain of a chart $ξ$ of $M$; $ω$ is a $C^{p}$-action on $W$ parametrized by $A$. Via a result in \\cite{sil09261621}, we construct $\\mathfrak{A}:\\mathfrak{Z}^{O}\\times A\\to\\mathcal{M}(W,\\mathcal{Z})$ where $\\mathfrak{A}(u,η)$ is the action functional associated with $\\mathscr{L}$, $u$ and $η$. Here $\\mathcal{M}(W,\\mathcal{Z})=\\mathcal{L}_{s}(\\mathcal{H}(W),\\mathcal{Z})$ is the lcs of measures on $W$ and valued in $\\mathcal{Z}$. By letting $\\mathcal{A}(u):A\\to\\mathcal{M}(W,\\mathcal{Z})$ be such that $\\mathcal{A}(u)(η)=\\mathfrak{A}(u,η)$, we state that $\\mathcal{A}(u)$ is differentiable off-shell, find its differential map off and on-shell. We establish that if the differential map of $\\mathcal{A}(u)$ on $0$ is $0$, then $\\mathscr{N}[u]$ is conserved on-shell, and if $p=\\infty$, then the divergence of $\\mathscr{N}[u]$ equals $0$, where the divergence of a lcs valued vector field is defined and analyzed in \\cite{sil09261621}. Here $\\mathscr{N}[u]$ is a $\\mathcal{L}_{b}(T,\\mathcal{Z})$-valued $C^{(p-1)}$-vector field of $M$ on $U=ξ(W)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09137",
  "author_total": 1,
  "authors": [
    {
      "name": "Benedetto Silvestri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3wcdsp87m2ye3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09137",
  "fulltext_url": null,
  "id": "3wcdsp87m2ye3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09137",
  "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.FA"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7221060550",
  "pdf_url": "https://arxiv.org/pdf/2610.09137",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3wcdsp87m2ye3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09137",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09137"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Universal operatorial Noether current associated with a quasi-complete locally convex linear space valued Lagrangian defined on an open set of a product of normed spaces",
  "title_text": "Universal operatorial Noether current associated with a quasi-complete locally convex linear space valued Lagrangian defined on an open set of a product of normed spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/3wcdsp87m2ye3",
  "venue": "arXiv",
  "versions": []
}