Geodesic
Martin boundary associated with a system of PDE
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 399-425.

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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 $.
Classification : 31B10, 31B30, 31C35, 35C15, 35J40, 60J50
Keywords: Martin boundary; biharmonic functions; coupled partial differential equations 
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     author = {Benyaiche, Allami and Ghiate, Salma},
     title = {Martin boundary associated with a system of {PDE}},
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     zbl = {1132.31005},
     language = {en},
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Benyaiche, Allami; Ghiate, Salma. Martin boundary associated with a system of PDE. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 399-425. http://geodesic.mathdoc.fr/item/CMUC_2006__47_3_a3/