Let $R$ be a Riemannian manifold without a biharmonic Green function defined on it and $\Omega $ a domain in $R$. A necessary and sufficient condition is given for the existence of a biharmonic Green function on $\Omega $.
@article{119392,
author = {Sadoon Ibrahim Othman and Victor Anandam},
title = {Biharmonic Green domains in a Riemannian manifold},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {44},
year = {2003},
pages = {359-365},
zbl = {1127.31301},
mrnumber = {2026170},
language = {en},
url = {http://dml.mathdoc.fr/item/119392}
}
Othman, Sadoon Ibrahim; Anandam, Victor. Biharmonic Green domains in a Riemannian manifold. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 359-365. http://gdmltest.u-ga.fr/item/119392/
Biharmonic Green functions in a Riemannian manifold, Arab J. Math. Sc. 4 (1998), 39-45. (1998) | MR 1679626 | Zbl 0942.31005
Biharmonic Green domains in $\Bbb R^n$, Hokkaido Math. J. 27 (1998), 669-680. (1998) | MR 1662962
Biharmonic classification of harmonic spaces, Rev. Roumaine Math. Pures Appl. 45 (2000), 383-395. (2000) | MR 1840160 | Zbl 0990.31003
Fonctions sousharmoniques associées à une mesure, Stud. Cerc. Şti. Mat. Iaşi 2 (1951), 114-118. (1951) | MR 0041989 | Zbl 0081.31601
Axiomatique des fonctions harmoniques, Les presses de l'Université de Montréal, 1966. | MR 0247124 | Zbl 0148.10401
An axiomatic treatment of pairs of elliptic differential equations, Ann. Inst. Fourier 16 (1966), 167-208. (1966) | MR 0227455 | Zbl 0172.15101
Liouville-Picard theorem in harmonic spaces, Hiroshima Math. J. 28 (1998), 501-506. (1998) | MR 1657539 | Zbl 0915.31008
Classification theory of Riemannian manifolds, Lecture Notes in Math. 605, Springer-Verlag, 1977. | MR 0508005 | Zbl 0355.31001