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Deterministic KPZ-type equations with nonlocal “gradient terms”

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dc.contributor.authorAbdellaou, Boumediene
dc.contributor.authorFernández, Antonio J.
dc.contributor.authorLeonori, Tommaso
dc.contributor.authorYounes, Abdelbadie
dc.contributor.orcidhttps://orcid.org/0000-0002-0848-4463
dc.contributor.orcidhttps://orcid.org/0000-0001-6236-2769
dc.date.accessioned2024-11-19T09:50:40Z
dc.date.available2024-11-19T09:50:40Z
dc.date.issued2023-12-03
dc.description.abstracten
dc.description.abstractThe main goal of this paper is to prove existence and non-existence results for deterministic Kardar–Parisi–Zhang type equations involving non-local “gradient terms”. More precisely, let Ω ⊂ RN, N≥ 2 , be a bounded domain with boundary ∂Ω of class C2. For s∈ (0 , 1) , we consider problems of the form (Formula presented.) where q> 1 and λ> 0 are real parameters, f belongs to a suitable Lebesgue space, μ∈ L∞(Ω) and D represents a nonlocal “gradient term”. Depending on the size of λ> 0 , we derive existence and non-existence results. In particular, we solve several open problems posed in [Abdellaoui in Nonlinearity 31(4): 1260-1298 (2018), Section 6] and [Abdellaoui in Proc Roy Soc Edinburgh Sect A 150(5): 2682-2718 (2020), Section 7]. © 2022, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.
dc.description.versionversión final
dc.identifier.citationAbdellaoui, B., Fernández, A.J., Leonori, T. et al. Deterministic KPZ-type equations with nonlocal “gradient terms”. Annali di Matematica 202, 1451–1468 (2023). https://doi.org/10.1007/s10231-022-01288-6
dc.identifier.doihttp://doi.org/10.1007/s10231-022-01288-6
dc.identifier.issn0373-3114; e-ISSN: 1618-1891
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24423
dc.journal.issue3
dc.journal.titleAnnali di Matematica Pura ed Applicata
dc.journal.volume202
dc.language.isoen
dc.page.final1468
dc.page.initial1451
dc.publisherSpringer Nature
dc.relation.centerFacultades y escuelas::Facultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsDeterministic KPZ–type equationsen
dc.subject.keywordsFractional Laplacianen
dc.subject.keywordsNonlocal “gradient terms”en
dc.titleDeterministic KPZ-type equations with nonlocal “gradient terms”en
dc.typeartículoes
dc.typejournal articleen
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