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Martin boundary associated with a system of PDE

Allami Benyaiche; Salma Ghiate — 2006

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. $▵^{2} ϕ = 0$ ) and for non negative solutions of the equation $▵^{2} ϕ = ϕ$ .

Thinness and non-tangential limit associated to coupled PDE

Allami Benyaiche; Salma Ghiate — 2013

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. $▵^{2} ϕ = 0$ ) and equations of $▵^{2} ϕ = ϕ$ type.

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