Calculation of Green's function for Poisson's equation on a semi-disk using a Fourier transform in the radial variable

. A new calculation of Green’s function for the problem with Poisson’s equation on a semi-disk under mixed Dirichlet-Neumann boundary conditions is presented. The method consists in (cid:28)rst (a) employing a Fourier transform in the radial variable to calculate the solution of the simpler problem that is obtained with the homogenization of the boundary conditions, and then (b) inferring the desired Green’s function by comparing the expression of this calculated solution with the one given by Green’s formula. The solution that the method yields is elaborated to the point of having the same closed form that the method of images provides.