| Popis: |
In this article we obtain positive singular solutions of (1) − Δ u = | ∇ u | p in Ω , u = 0 on ∂ Ω , where Ω is a small C 2 perturbation of the unit ball in R N . For N N − 1 p 2 we prove that if Ω is a sufficiently small C 2 perturbation of the unit ball there exists a singular positive weak solution u of (1) . In the case of p > 2 we prove a similar result but now the positive weak solution u is contained in C 0 , p − 2 p − 1 ( Ω ‾ ) and yet is not in C 0 , p − 2 p − 1 + e ( Ω ‾ ) for any e > 0 . |
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