Boundary singularities of solutions of N-harmonic equations with absorption

Rouba Borghol (1) , Laurent Veron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the boundary behaviour of solutions u of $− \Delta_Nu + |u|^{q−1}u = 0$ in a bounded smooth domain $\Omega ⊂ R^N$ subject to the boundary condition u = 0 except at one point, in the range $q >N−1$.We prove that if $q \geq 2N −1$ such an u is identically zero, while, if $N −1

Mots clés: N-Harmonic operator; Conformal invariance; Hopf lemma; Strong maximum principle

Domaines: Equations aux dérivées partielles [math.AP]

Rouba Borghol, Laurent Veron. Boundary singularities of solutions of N-harmonic equations with absorption. Journal of Functional Analysis, 2006, 241, pp.611-637. ⟨hal-00281624⟩