Previous |  Up |  Next

Article

Keywords:
biharmonic Green functions
Summary:
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 $.
References:
[1] Anandam V.: Biharmonic Green functions in a Riemannian manifold. Arab J. Math. Sc. 4 (1998), 39-45. MR 1679626 | Zbl 0942.31005
[2] Anandam V., Damlakhi M.: Biharmonic Green domains in $\Bbb R^n$. Hokkaido Math. J. 27 (1998), 669-680. MR 1662962
[3] Anandam V.: Biharmonic classification of harmonic spaces. Rev. Roumaine Math. Pures Appl. 45 (2000), 383-395. MR 1840160 | Zbl 0990.31003
[4] Brelot M.: Fonctions sousharmoniques associées à une mesure. Stud. Cerc. Şti. Mat. Iaşi 2 (1951), 114-118. MR 0041989 | Zbl 0081.31601
[5] Brelot M.: Axiomatique des fonctions harmoniques. Les presses de l'Université de Montréal, 1966. MR 0247124 | Zbl 0148.10401
[6] Loeb P.A.: An axiomatic treatment of pairs of elliptic differential equations. Ann. Inst. Fourier 16 (1966), 167-208. MR 0227455 | Zbl 0172.15101
[7] Othman S.I., Anandam V.: Liouville-Picard theorem in harmonic spaces. Hiroshima Math. J. 28 (1998), 501-506. MR 1657539 | Zbl 0915.31008
[8] Sario L., Nakai M., Wang C., Chung L.O.: Classification theory of Riemannian manifolds. Lecture Notes in Math. 605, Springer-Verlag, 1977. MR 0508005 | Zbl 0355.31001
Partner of
EuDML logo