Abstract :
The representation u(x) = F2(x)Qm-2(x)+Qm(x) for the solution to the Dirichlet problem for the Laplace equation in a disk: F2(x) = jx - x0j2 - c2 6 0, is proved using the Poisson integral; Qm(x) being the polynomial boundary function of degree m, Qm-2(x) being the uniquely determined polynomial of degree m - 2.
Keyword :
the Dirichlet problem, the Poisson integral