A relation between two biharmonic Green’s functions on Riemannian manifolds
Dennis Hada · Transactions of the American Mathematical Society · 1977
The biharmonic Green’s function γ \gamma whose values and Laplacian are identically zero on the boundary of a region and the biharmonic Green’s function Γ \Gamma whose values and normal derivative vanish on the boundary originated in the investigation of thin plates whose edges are simply supported or clamped, respectively. A relation between these two biharmonic Green’s functions known for planar regions is extended to Riemannian manifolds thereby establishing that any Riemannian manifold for which γ \gamma exists must also carry Γ \Gamma .