Chapter 14.8, Problem 51E

Green’s Second Identity Prose Green’s Second Identity for scalar-valued functions u and v defined on a region D:

${\displaystyle \underset{D}{\iiint }\left(u{\nabla }^{2}v-v{\nabla }^{2}u\right)dV=}{\displaystyle \underset{S}{\iint }\left(u\nabla v-v\nabla u\right)\cdot ndS.}$

  (Hint: Reverse the roles of u and v in Green’s First Identity.)