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wedge-like domains

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Boundary singularities on a wedge-like domain of a semilinear elliptic equation
Part of
- Elliptic equations and systems
Konstantinos T. Gkikas
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 5 / October 2015

Published online by Cambridge University Press:

21 July 2015, pp. 979-1006

Print publication:

October 2015
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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.