{
  "abstract": "We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the controls are the amplitudes of these singular sources. We prove existence and uniqueness of an optimal solution and derive first-order optimality conditions. We then propose a discretization based on finite elements. Since the set of admissible controls is finite dimensional, the control variable itself does not require discretization. We conclude by deriving a priori error bounds",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27776",
  "author_total": 2,
  "authors": [
    {
      "name": "Enrique Otarola"
    },
    {
      "name": "Abner J. Salgado"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05k8kf86dk73c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27776",
  "fulltext_url": null,
  "id": "05k8kf86dk73c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27776",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7204748087",
  "pdf_url": "https://arxiv.org/pdf/2608.27776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05k8kf86dk73c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27776"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal control of fractional diffusion with Dirac measures",
  "title_text": "Optimal control of fractional diffusion with Dirac measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/05k8kf86dk73c",
  "venue": "arXiv",
  "versions": []
}