I am from chemistry background, trying to grasp application of Green's function. In the book "Application of Green's function in Science and Engineering" by MD Greenberg, on page 58-59, Following is written:
Whereas $u =0$ on C (boundary condition), the normal derivative $u_n$ is not specified, and hence need not be zero. For the boundary terms to vanish we therefore need $v=0$.
Why? I mean why can't we assume that $u_n$ might not be zero, but we have no problem in assuming $v=0$?
Also being tangentially on same topic, on page 57 following is given which is not clear, $(v\nabla u - u\nabla v).\textbf{n} = v\partial u/\partial n - u\partial v/ \partial n$
I can't understand how?