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

Moshe Marcus; Laurent Veron

paper

Maximal solutions for $- Δ u + u^{q} = 0$ in open or finely open sets

arXiv:0810.1667

Abstract

We study the existence and uniqueness of new classes of solutions of the superlinear equation $- Δ u + u^{q} = 0$ (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.

A paraître au Journal de Mathématiques Pures et Appliquées

Maximal solutions for −Δu+uq=0 in open or finely open sets

Abstract

Maximal solutions for $- Δ u + u^{q} = 0$ in open or finely open sets