Volume no :5, Issue no: 2, May (2011)

Journal of Pure and Applied Mathematics: Advances and Applications

FOURIER-LIKE SOLUTION OF THE DIRICHLET PROBLEM FOR THE LAPLACE EQUATION IN K-TYPE GIELIS DOMAINS

Author's: Diego Caratelli, Johan Gielis and Paolo E. Ricci
Pages: [99] - [111]
Received Date: March 10, 2011
Submitted by:

Abstract

The interior and exterior Dirichlet problems for the Laplace equation in k-type Gielis domains are analytically addressed by using a suitable Fourier-like technique. A dedicated numerical procedure based on the computer-aided algebra tool Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. Computed results are found to be in good agreement with theoretical findings on Fourier series expansion presented by Carleson.

Keywords

Laplace equation, Dirichlet problem, k-type Gielis domain.