{
  "abstract": "In this paper, a general principle for coercivity in optimal control problems is investigated. Utilizing regularity properties of solutions to second-order elliptic PDEs on Lipschitz domains, we provide quantitative sufficient second-order optimality condition for control-constrained semilinear elliptic optimal control problems. The main property of the investigated optimal control problems is the absence of a Tikhonov regularization term on the objective function. For these problems, the second variation is a quadratic form in the linearized state, and its curvature function may vanish or change sign. The quantitative condition we introduce implies coercivity with respect to the $L^2$-norm of the linearized-states. As a consequence, the stability of the sufficient second-order condition under perturbations of the states and the tracking data is shown.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14525",
  "author_total": 2,
  "authors": [
    {
      "name": "Francisco Fuica"
    },
    {
      "name": "Nicolai Jork"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cafvtfhzn4y2v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14525",
  "fulltext_url": null,
  "id": "cafvtfhzn4y2v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14525",
  "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.OC"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7203627775",
  "pdf_url": "https://arxiv.org/pdf/2608.14525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cafvtfhzn4y2v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2608.14525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On quantitative sufficient second-order optimality conditions for elliptic optimal control problems",
  "title_text": "On quantitative sufficient second-order optimality conditions for elliptic optimal control problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/cafvtfhzn4y2v",
  "venue": "arXiv",
  "versions": []
}