{
  "abstract": "In this paper we prove the existence, uniqueness and regularity of classical solutions \\break of a semilinear parabolic equation with a mixed local and nonlocal diffusion operator \\break $\\mathcal{L} = -(-Δ)^s + Δ$ and Dirichlet boundary conditions. Here, $(-Δ)^s$ is the integral fractional laplacian and $Δ$ is the classic local laplacian. We then study the interior regularity of said solutions and conclude that they are Hölder continuous in both space and time, and they are $C^{2,α}_{loc}$ in space for all positive times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06537",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergio Junquera"
    },
    {
      "name": "Leandro M. Del Pezzo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fnq6syx80f315.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06537",
  "fulltext_url": null,
  "id": "fnq6syx80f315",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06537",
  "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"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220735270",
  "pdf_url": "https://arxiv.org/pdf/2610.06537",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fnq6syx80f315.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.06537",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06537"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior regularity of mixed local-nonlocal parabolic semilinear equations",
  "title_text": "Interior regularity of mixed local-nonlocal parabolic semilinear equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/fnq6syx80f315",
  "venue": "arXiv",
  "versions": []
}