Large solutions to quasilinear problems involving the p-Laplacian as p diverges

In this paper we deal with large solutions to {−Δ+|∇|=()=+∞ in Ω, on ∂Ω, where Ω⊂ℝ , with ≥1, is a smooth, open, connected, and bounded domain, ≥2, >0, −1<≤ and ∈(Ω)∩∞(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.