- #1
bobbarker
- 8
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Homework Statement
"Let huv = 0 [tex]\forall[/tex] u, v. Show that h is of the form h(u,v) = U(u) + V(v)."
Homework Equations
n/a
The Attempt at a Solution
The problem doesn't really seem that complex to me, in fact, from PDEs a few years ago I remember this quite readily. However, the proof/demonstration is giving me some trouble. I started off supposing that huv = 0 [tex]\forall[/tex] u,v but h were of the form h(u,v) = U(u)*V(v). Then
hu(u,v) = U'(u)*V(v)
huv(u,v) = U'(u)*V'(v) = 0
But that just means that either/both U,V are constants, which isn't prohibited in the initial setup of the problem.
Any ideas? Thanks! :)