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. $\triangle ^{2}\varphi =0$) and for non negative solutions of the equation $\triangle ^{2}\varphi =\varphi $.

Keywords: Martin boundary, biharmonic functions, coupled partial differential equations
AMS Subject Classification: Primary 31C35; Secondary 31B30, 31B10, 60J50