My equation is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left(\mathbf{\nabla}\sigma\right)\cdot\left(\mathbf{\nabla}V\right) + \sigma\nabla^2V = 0[/tex]

If I'm given V(r) on the boundary of some volume, and I know σ(r) inside the volume, is there a unique solution V(r) inside that volume for any arbitrary (well-behaved) function σ(r)?

I suspect the answer is yes, but I've never taken a formal PDE class, so I wanted to double-check.

Edit: just so it's clear, I don't need to know how to solve for V, I just need to know that it's possible to find V in principle.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# PDE Existence/Uniqueness Question

Loading...

Similar Threads for Existence Uniqueness Question |
---|

I Question about second order linear differential equations |

B Simple double integration of square wave question |

I Question regarding integration of an equation |

A Some questions regarding the ADI Method |

I Quick Differential Form Question |

**Physics Forums | Science Articles, Homework Help, Discussion**