Maximal solutions for $-\Delta u+u^q=0$ in open or finely open sets

Moshe Marcus (1) , Laurent Veron (2)

1 TECHNION - Department of Mathematics
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the existence and uniqueness of new classes of solutions of the superlinear equation $-\Delta u+u^q=0$ (q>1) in a domain of R^N or in a finely open set for the topology associated to the Bessel capacity C_{2,q'}. Condition of existence or uniqueness of solutions with boundary blow-up are obtained generalizing the results of Dhersin-Le Gall and of Labutin.

Mots clés: Bessel capacities; Wiener type test; fine topology; sigma moderate solutions

Domaines: Equations aux dérivées partielles [math.AP]

Moshe Marcus, Laurent Veron. Maximal solutions for $-\Delta u+u^q=0$ in open or finely open sets. Journal de Mathématiques Pures et Appliquées, 2009. ⟨hal-00328094v3⟩