- #1

draco193

- 7

- 0

## Homework Statement

Use Divergence theorem to determine an alternate formula for [tex]\int\int u \nabla^2 u dx dy dz[/tex] Then use this to prove laplaces equation [tex]\nabla^2 u = 0[/tex] is unique. u is given on the boundary.

## Homework Equations

[tex]u \nabla^2 u = \nabla * (u \nabla u) -(\nabla u)^2[/tex]

## The Attempt at a Solution

Using Divergence theorem, I get that the new equation should be [tex]\oint (u \nabla u) *n -\oint (\nabla u)^2[/tex] where n is the normal vector.

I wanted to make sure that I had applied this correctly before moving onto the next part.

My plan for the next part would then be to say that u=v-w, where v and w are arbitrary vectors, and show that v =w to show uniqueness of u.