Boundary singularities of solutions of N-harmonic equations with absorption

We study the boundary behaviour of solutions u of −ΔNu+|u|^q−1u=0 in a bounded smooth domain Ω⊂RN subject to the boundary condition u=0 except at one point, in the range q>N−1. We prove that if q?2N−1 such an u is identically zero, while, if N−1<q<2N−1, u inherits a boundary behaviour which either corresponds to a weak singularity, or to a strong singularity. Such singularities are effectively constructed.