surface and partial dervatives PRoof

Hi,

Guidance is appreciated.Thanks.

Prove that ∫∫∫_{v}∇f.∇gdV+∫∫∫_{v}f∇²gdV=∫∫_{s}f∇g.ndS

V is closed bounded region in space ,whose boundary is piecewise smooth orientable surface S.

n is an outwards pointing unit normal vector to S.

f and g are scalar functions with continuous second partial derivatives.

Re: surface and partial dervatives Proof

This is actually a simple application of the generalized Stokes' Theorem.

All you need to prove is that , where I've used angle brackets to denote the inner product.