# Dirichlet problem

Suppose $\mathrm{\Omega}$ is a domain of ${\mathbb{R}}^{n}$ and $\partial \mathrm{\Omega}$ is the boundary of $\mathrm{\Omega}$.
Further suppose $f$ is a function $f:\partial \mathrm{\Omega}\to \u2102$. Then the
*Dirichlet problem ^{}* is to find a function $\varphi :\mathrm{\Omega}\cup \partial \mathrm{\Omega}\to \u2102$
such that

$\varphi $ | $=$ | $f,\text{on}\partial \mathrm{\Omega},$ | ||

${\nabla}^{2}\varphi $ | $=$ | $0,\text{in}\mathrm{\Omega}.$ |

Title | Dirichlet problem |
---|---|

Canonical name | DirichletProblem |

Date of creation | 2013-03-22 14:57:06 |

Last modified on | 2013-03-22 14:57:06 |

Owner | matte (1858) |

Last modified by | matte (1858) |

Numerical id | 7 |

Author | matte (1858) |

Entry type | Definition |

Classification | msc 31B05 |

Classification | msc 31A05 |

Classification | msc 31B15 |

Related topic | HarmonicFunction |