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

Abstract

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.