Boundary singularities of solutions of N-harmonic equations with absorption

الأصل · EN

We study the boundary behaviour of solutions u of -Δₙu+ |u|q⁻¹u=0 in a bounded smooth domain Ωⁿ 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 a 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.