Green Functions for the Biharmonic Operator

Convolution of harmonic Green functions leads to different hybrid higher order polyharmonic Green functions. They differ from the related polyharmonic Green–Almansi function and are linked to different boundary value problems. The advantage of convoluted higher order Green functions is that they allow to decompose the boundary value problem for a linear higher order Poisson equation into some for a system of fist order Poisson equations. The higher the order the greater is the variety of possible boundary value problems and related hybrid Green functions. The situation is explained here just for the biharmonic operator. In order to be explicit just the unit disc is treated.