Published online by Cambridge University Press: 20 September 2012
Let λ* > 0 denote the largest possible value of λ such that the system
has a solution, where is the unit ball in ℝn centred at the origin, p > 1 and n is the exterior unit normal vector. We show that for λ = λ* this problem possesses a unique weak solution u*, called the extremal solution. We prove that u* is singular when n ≥ 13 for p large enough and actually solve part of the open problem which Dávila et al. left unsolved.