Buccheri, StefanoLeonori, Tommaso2024-11-202024-11-202021-01-18Buccheri, S., Leonori, T. Large solutions to quasilinear problems involving the p-Laplacian as p diverges. Calc. Var. 60, 30 (2021). https://doi.org/10.1007/s00526-020-01883-60944-2669; e-ISSN: 1432-0835https://doi.org/10.1007/s00526-020-01883-6https://hdl.handle.net/20.500.14468/24434In this paper we deal with large solutions to {u-Δpu+β|∇u|q=finΩ,u(x)=+∞on∂Ω,where Ω ⊂ RN , with N≥ 1 , is a smooth, open, connected, and bounded domain, p≥ 2 , β> 0 , p- 1 < q≤ p and f∈ C(Ω) ∩ L∞(Ω). We are interested in studying their behavior as p diverges. Our main result states that, if, in some sense, the domain Ω is large enough, such solutions converge locally uniformly to a limit function that turns out to be a large solution of a suitable limit equation (that involves the ∞-Laplacian). Otherwise, if Ω is small, we have a complete blow-up.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículo