Geodesic
Martin boundary associated with a system of PDE
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 3, pp. 399-425 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $.
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 
@article{CMUC_2006_47_3_a3,
     author = {Benyaiche, Allami and Ghiate, Salma},
     title = {Martin boundary associated with a system of {PDE}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {399--425},
     year = {2006},
     volume = {47},
     number = {3},
     mrnumber = {2281003},
     zbl = {1132.31005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a3/}
}
TY  - JOUR
AU  - Benyaiche, Allami
AU  - Ghiate, Salma
TI  - Martin boundary associated with a system of PDE
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 399
EP  - 425
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a3/
LA  - en
ID  - CMUC_2006_47_3_a3
ER  - 
%0 Journal Article
%A Benyaiche, Allami
%A Ghiate, Salma
%T Martin boundary associated with a system of PDE
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 399-425
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_2006_47_3_a3/
%G en
%F CMUC_2006_47_3_a3
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/