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.
Guidance is appreciated.Thanks.
Prove that ∫∫∫v∇f.∇gdV+∫∫∫vf∇²gdV=∫∫sf∇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.