The Robin problem for the Laplace equation in a three-dimensional starlike domain

Abstract

Abstract The internal and external Robin problems for the Laplace equation in bounded starlike domains are addressed. We show how to derive the relevant solutions by using a suitable Fourier series-like method. Numerical results are specifically obtained considering three-dimensional domains whose boundary is defined by a generalization of the so-called “superformula” introduced by Gielis. By using the computer algebra code Mathematica©, truncated series approximations of the solutions are determined. Our findings are in good agreement with the theoretical results on the Fourier series due to Carleson.