Boundary singularities of N -harmonic functions

Rouba Borghol (1) , Laurent Veron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We characterize the boundary behaviour of any positive N-harmonic function $u$ in a smooth domain $\Omega$ which vanishes on $\partial\Omega\setminus\{a\}$. We also give new explicit separable expression for singular of regular p-harmonic functions.

Mots clés: Singularities; Boundary Harnack inequalities; Conformal transformations; Hopf boundary lemma; Maximum principle; Separable solutions; Singularities.

Domaines: Equations aux dérivées partielles [math.AP]

Rouba Borghol, Laurent Veron. Boundary singularities of N -harmonic functions. Communications in Partial Differential Equations, 2007, 32, pp.1001-1015. ⟨hal-00281615⟩