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

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

2008-10-09

arxiv.org/abs/0810.1667v3

Mathematics

Analysis of PDEs

A para\^itre au Journal de Math\'ematiques Pures et Appliqu\'ees

Scientific paper

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.

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