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Boundary singularities on a wedge-like domain of a semilinear elliptic equation

Published online by Cambridge University Press:  21 July 2015

Konstantinos T. Gkikas*
Affiliation:
Centro de Modelamiento Matemático Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago, Chile, (kgkikas@dim.uchile.cl)

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

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