Cases when the solution of the Dirichlet problem for the Laplace equation on a polygon is a polynomial. (Q1432479)

This paper is concerned with the Dirichlet problem for an arbitrary polygonal region in the plane, where the boundary values are given by algebraic polynomials along the edges. The aim is to determine whether or not the solution to the problem is a polynomial and, if it is, to find it. The approach involves constructing a test harmonic polynomial and checking whether it satisfies the given boundary conditions. No details are provided.