ON A REPRESENTATION OF THE SOLUTION TO THE DIRICHLET PROBLEM IN A DISK. THE POISSON INTEGRAL BASED SOLUTION IN POLYNOMIALS

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.

Keywords

• the Dirichlet problem, the Poisson integral