Boundary singularities on a wedge-like domain of a semilinear elliptic equation
Published online by Cambridge University Press: 21 July 2015
Abstract
Let n ≥ 2 and let be a Lipschitz wedge-like domain. We construct positive weak solutions of the problem
that vanish in a suitable trace sense on ∂Ω, but which are singular at a prescribed ‘edge’ of Ω if p is equal to or slightly above a certain exponent p0 > 1 that depends on Ω. Moreover, for the case in which Ω is unbounded, the solutions have fast decay at infinity.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 5 , October 2015 , pp. 979 - 1006
- Copyright
- Copyright © Royal Society of Edinburgh 2015
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