A POLYHARMONIC DIRICHLET PROBLEM OF ARBITRARY ORDER FOR COMPLEX PLANE DOMAINS

The consecutive convolution of the harmonic Green function with itself provides a polyharmonic Green function of any order. Convoluting such a polyharmonic Green function with a polyharmonic Green-Almansi function gives a polyharmonic Green function of new type. It leads to a certain Dirichlet problem for a Poisson equation of certain order. This problem is well-posed. Its solution is given here.