{
  "abstract": "This work provides a framework to treat optimal control problems on separable Banach spaces in the viscosity sense. First, it extends the notion of $B$-viscosity solutions to the Banach setting and relates the extension to the notions of viscosity solutions used in metric space settings. As the main results, the paper proves a strict comparison principle and characterizes the value function of an optimal control problem as the unique viscosity solution to an infinite-dimensional HJB equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18496",
  "author_total": 1,
  "authors": [
    {
      "name": "Fabian Fuchs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7xr1ngnsq5ma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18496",
  "fulltext_url": null,
  "id": "a7xr1ngnsq5ma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18496",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W7221751353",
  "pdf_url": "https://arxiv.org/pdf/2610.18496",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7xr1ngnsq5ma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18496",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18496"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces",
  "title_text": "Viscosity Solutions for Hamilton-Jacobi equations on Separable Banach Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/a7xr1ngnsq5ma",
  "venue": "arXiv",
  "versions": []
}