# Thread: Reference for a derivation of the multidimensional integration by parts formula

1. ## Reference for a derivation of the multidimensional integration by parts formula

The general integration by parts formula in multiple dimensions is given by

$\int_{\Omega} \nabla u \cdot \mathbf{v} = \int_{\partial\Omega} (u \mathbf{v})\cdot n-\int_\Omega u \nabla\cdot\mathbf{v}$

Is there a good reference that details the derivation of this formula? More specifically, I'm looking for a derivation of the above result that does not use differential forms.

Thanks.

2. I found a reference that develops the formula in a general setting:

Integration on infinite-dimensional ... - Google Books

This comes from the book, "Integration on Infinite-Dimensional Surfaces and Its Applications," by Uglanov.

Integration on Infinite-Dimensional Surfaces and Its Applications

I've not had an opportunity to obtain the book, but from a quick glance, this appears to be the sort of derivation that I'm looking for.

For the time being, I'll leave the thread as unresolved in case someone has a different reference they've found useful.