Biharmonic Green functions on homogeneous trees (Q1038594)

The authors study the simply-supported and the clamped biharmonic Green functions with respect to both Laplacians. The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk \(D\) in \(C\) arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a local placed at another point.