{
  "abstract": "We investigate the regularity of viscosity solutions to a class of nonlocal Hamilton-Jacobi equations driven by x-dependent integro-differential operators and coercive superlinear Hamiltonians. We first establish Hölder regularity for bounded viscosity solutions under general structural and continuity assumptions on the underlying Lévy measures, without imposing any ellipticity condition on the nonlocal operator. The Hölder exponent is given explicitly in terms of the order σ ∈ (0, 2) of the operator and the growth exponent m > 1 of the Hamiltonian. In particular, our approach applies to arbitrary superlinear Hamiltonians, including the delicate regime 1 < m < σ < 2, and yields an improved regularity exponent when σ ∈ (1, 2). Assuming in addition a weak ellipticity condition on the nonlocal operator, we prove that viscosity solutions are globally Lipschitz continuous. The proof combines the Hölder regularity supplied by the coercive Hamiltonian with the regularizing effect of the nonlocal diffusion through an Ishii-Lions argument, allowing us to treat Hamiltonians with arbitrary superlinear growth. Finally, we provide a counterexample showing that, in the absence of ellipticity, Lipschitz regularity may fail if the spatial dependence of the Lévy measures is merely Hölder continuous, thereby illustrating the sharpness of our continuity assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16918",
  "author_total": 4,
  "authors": [
    {
      "name": "Adina Ciomaga"
    },
    {
      "name": "Tri Minh Lê"
    },
    {
      "name": "Olivier Ley"
    },
    {
      "name": "Erwin Topp"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6x6fza2qgphq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16918",
  "fulltext_url": null,
  "id": "e6x6fza2qgphq",
  "issns": [],
  "landing_url": "https://hal.science/hal-05737933v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
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      "0.math"
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      "hal",
      "1.math.math-ap"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05737933/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6x6fza2qgphq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05737933",
      "source": "hal",
      "url": "https://hal.science/hal-05737933v1"
    },
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16918"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Improved Regularity for Nonlocal Hamilton--Jacobi Equations with Superlinear Hamiltonians",
  "title_text": "Improved Regularity for Nonlocal Hamilton--Jacobi Equations with Superlinear Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/e6x6fza2qgphq",
  "venue": "HAL",
  "versions": []
}