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Martin boundary associated with a system of PDE

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Allami Benyaiche, Salma Ghiate

Martin boundary associated with a system of PDE

Comment.Math.Univ.Carolin. 47,3 (2006) 399-425.

Abstract: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. 42ϕ= 0) and for non negative solutions of the equation42ϕ=ϕ.

Keywords: Martin boundary, biharmonic functions, coupled partial differential equations

AMS Subject Classification: Primary 31C35; Secondary 31B30, 31B10, 60J50

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