Boundary singularities of solutions of N-harmonic equations with absorption

摘要

We study the boundary behaviour of solutions u of -Delta(N)u + vertical bar u vertical bar(q-1)u = 0 in a bounded smooth domain Omega subset of R-N subject to the boundary condition u = 0 except at one point, in the range q > N - 1. We prove that if q >= 2N - I such an it 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. (c) 2006 Elsevier Inc. All rights reserved.