# Laplace equation

The scalar form of *Laplace’s equation* is the partial differential equation^{}

$${\nabla}^{2}f=0$$ |

and the vector form is

$${\nabla}^{2}\mathbf{A}=0,$$ |

where ${\nabla}^{2}$ is the Laplacian. It is a special case of the Helmholtz differential equation^{} with $k=0.$

A function $f$ which satisfies Laplace’s equation is said to be *harmonic*. Since Laplace’s equation is linear, the superposition of any two solutions is also a solution.

Title | Laplace equation |
---|---|

Canonical name | LaplaceEquation |

Date of creation | 2013-03-22 13:09:11 |

Last modified on | 2013-03-22 13:09:11 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 7 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 26B12 |

Synonym | Laplace differential equation |

Related topic | PoissonsEquation |

Related topic | ExampleOfSolvingTheHeatEquation |

Defines | harmonic |