Martin boundary associated with a system of PDE

Allami Benyaiche; Salma Ghiate

Commentationes Mathematicae Universitatis Carolinae (2006)

  • Volume: 47, Issue: 3, page 399-425
  • ISSN: 0010-2628

Abstract

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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. ▵ 2 ϕ = 0 ) and for non negative solutions of the equation ▵ 2 ϕ = ϕ .

How to cite

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Benyaiche, Allami, and Ghiate, Salma. "Martin boundary associated with a system of PDE." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 399-425. <http://eudml.org/doc/249874>.

@article{Benyaiche2006,
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 $.},
author = {Benyaiche, Allami, Ghiate, Salma},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Martin boundary; biharmonic functions; coupled partial differential equations; Martin boundary; biharmonic function},
language = {eng},
number = {3},
pages = {399-425},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Martin boundary associated with a system of PDE},
url = {http://eudml.org/doc/249874},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Benyaiche, Allami
AU - Ghiate, Salma
TI - Martin boundary associated with a system of PDE
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2006
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 47
IS - 3
SP - 399
EP - 425
AB - 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 $.
LA - eng
KW - Martin boundary; biharmonic functions; coupled partial differential equations; Martin boundary; biharmonic function
UR - http://eudml.org/doc/249874
ER -

References

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