Chapter 13.7, Problem 47PS

To determine

To prove: That ${\displaystyle \underset{S}{\int }{\displaystyle \int \frac{\partial u}{\partial n}dS}}={\displaystyle \underset{D}{\iiint }{\nabla }^{2}udV}$ ; where $u$ is a scalar function with continuous second partial derivatives in a region containing the solid region $D$ , with closed boundary surface $S$ .