{
  "abstract": "We study stability of semilinear exterior Dirichlet problems driven by possibly nonsymmetric Levy operators. Let $L^n$ and $L$ have Lévy-Khintchine symbols $ψ_n$ and $ψ$, respectively. Our basic assumption on the operators is that $ψ_n(ξ)\\toψ(ξ)$ for every $ξ\\in\\mathbb R^d$. Under mild regularity assumptions on the domain and an absolute-continuity condition for the resolvent of the limiting process, we prove pointwise and $L^p$-stability of solutions. No symmetry, uniform ellipticity, comparability of Lévy kernels, or common energy space is required; nonzero exterior data are allowed; and the monotone nonlinearity is subject to no growth restriction in the solution variable. The framework therefore covers local, nonlocal and mixed operators and, in particular, nonlocal-to-local limits, as well as fractional, relativistic, anisotropic and nonsymmetric stable-type operators. The proofs combine convergence of Lévy processes with a detailed analysis of exit times and exit positions and a stability theorem for monotone backward stochastic differential equations with varying terminal times. In the symmetric case, we also obtain Mosco convergence of the corresponding part forms on $C^0$ domains and give a counterexample showing that whole-space Mosco convergence need not pass to part forms on arbitrary open sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07963",
  "author_total": 3,
  "authors": [
    {
      "name": "Tomasz Klimsiak"
    },
    {
      "name": "Andrzej Rozkosz"
    },
    {
      "name": "Leszek Słomiński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e587xy7tgt5k1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07963",
  "fulltext_url": null,
  "id": "e587xy7tgt5k1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07963",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220962324",
  "pdf_url": "https://arxiv.org/pdf/2610.07963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e587xy7tgt5k1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability of Solutions to Semilinear Exterior Dirichlet Problems under Convergence of Lévy Symbols",
  "title_text": "Stability of Solutions to Semilinear Exterior Dirichlet Problems under Convergence of Lévy Symbols",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/e587xy7tgt5k1",
  "venue": "arXiv",
  "versions": []
}