| Version current |
Version 3 |
| Suppose $\Omega$ is a domain of $\sR^n$ and $\partial\Omega$ is the boundary of $\Omega$. |
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 |
Further suppose $f$ is a function $f\colon\partial \Omega\to\sC$. Then the |
| \emph{Dirichlet problem} is to find a function $\phi\colon \Omega\cup \partial \Omega \to\sC$ |
\emph{Dirichlet problem} is to find a function $\phi\colon \Omega\cup \partial \Omega \to\sC$ |
| such that |
such that |
| \begin{eqnarray*} |
\begin{eqnarray*} |
| \phi &=& f,\quad \text{on $\partial \Omega$}, \\ |
\phi &=& f,\quad \text{on $\partial \Omega$}, \\ |
|
\nabla^2 \phi &=& 0,\quad \text{in $\Omega$}.
|
\nabla^2 \phi &=& 0,\quad \text{in $\Omega$},
|
| \end{eqnarray*} |
\end{eqnarray*} |
