Properties of the extremal solution for a fourth-order elliptic problem
Published online by Cambridge University Press: 20 September 2012
Abstract
Let λ* > 0 denote the largest possible value of λ such that the system
has a solution, where is the unit ball in ℝn centred at the origin, p > 1 and n is the exterior unit normal vector. We show that for λ = λ* this problem possesses a unique weak solution u*, called the extremal solution. We prove that u* is singular when n ≥ 13 for p large enough and actually solve part of the open problem which Dávila et al. left unsolved.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 1051 - 1069
- Copyright
- Copyright © Royal Society of Edinburgh 2012
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