Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T10:48:14.563Z Has data issue: false hasContentIssue false

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, ([email protected])

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)