Existence of minimizing function

i try to show that the Dirichlet energy functional has a minimum subject to the constraint $\|u\|=1$.What do i have to do?

-
Wouldn't u(x) = [1 1 1 ... 1] / sqrt(n) satisfy your conditions? The gradient is zero everywhere... –  pedrosorio Nov 4 '12 at 14:03
You are spawning accounts like agent Smith in the second Matrix movie. Please consider registering your user. –  Asaf Karagila Nov 4 '12 at 14:51

@JamesBond: The problem is essentially the same, just use a constant function $u$ whose norm is g. Consider accepting correct answers when you ask a question. –  pedrosorio Nov 4 '12 at 14:55