Abdellaou, BoumedieneFernández, Antonio J.Leonori, TommasoYounes, Abdelbadie2024-11-192024-11-192023-12-03Abdellaoui, 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/s10231-022-01288-60373-3114; e-ISSN: 1618-1891http://doi.org/10.1007/s10231-022-01288-6https://hdl.handle.net/20.500.14468/24423The 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.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículodeterministic KPZ–type equationsfractional laplaciannonlocal “gradient terms”