Prove Dirichlet's principle for the Neumann boundary condition.  It
asserts that amoung all real-valued functions w(x) on D the quantity
E[w] = 1/2 (triple integral over D) |grad(w)|^2 dx - (double integral
over body of D) hw dS is the smallest for w = u, where u is the
solution of the Neumann problem
-laplace(u) = 0 in D, du/dn = h(x) on body D.  if the equations are
unclear please email me back. thanks

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Clarification of Question by awl-ga on 25 Nov 2002 09:44 PST

My friend an i have been debating the answer to the 3 other partial
differential equations problems that i have listed to pay 10 dollars
for an answer.  We placed a bet on it, and the questions shouldn't be
too hard for you to answer because me and my friend are only students,
and we just need another source to see who is right, and i would
really apreaciate it if we could get the answer by tomorrow morning.
thanks!

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Clarification of Question by awl-ga on 25 Nov 2002 09:50 PST

We will pay more if we get the questions answered by tomorrow, the
loser of the bet will pay so, please if you have time, help me prove
i'm right