Suppose $\Omega$ is a domain of $\sR^n$ and $\partial\Omega$ is the boundary of $\Omega$ . Further suppose $f$ is a function $f\colon\partial \Omega\to\sC$ . Then the Dirichlet problem is to find a function $\phi\colon \Omega\cup \partial \Omega \to\sC$ such that \begin{eqnarray*} \phi &=& f,\quad \text{on $\partial \Omega$}, \\ \nabla^2 \phi &=& 0,\quad \text{in $\Omega$}. \end{eqnarray*}