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

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  21 July 2015

Konstantinos T. Gkikas
Konstantinos T. Gkikas*
Affiliation:
Centro de Modelamiento Matemático Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago, Chile, ([email protected])
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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.

Keywords

prescribed boundary singularitiesvery weak solutioncritical exponentswedge-like domains

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J67: Boundary values of solutions to elliptic equations
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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