Abstract

We consider (Equation Presented) where γ > 0, f(u) = e u or f(u) = (1 + u) P, Γ 1 Γ 2 is a partition of ∂Ω and Ω ⊂ ℝ N. We determine sharp conditions on the dimension N and p > 1 such that the extremal solution is bounded, where the extremal solution refers to the one associated to the largest λ for which a solution exists.