Does ∇·(∇f × ∇g) = 0 require C² functions?

madachi · Apr 16, 2010

One of the basic vector identities is

[itex]\nabla \cdot (\nabla f \times \nabla g) = 0[/itex]

Is this true if [itex]f[/itex] and [itex]g[/itex] are [itex]C^{1}[/itex] ? (Or they must be [itex]C^{2}[/itex] functions?

Thanks!

phyzguy · Apr 16, 2010

I think this follows from the equality of mixed partial derivatives. So I think that f and g must be al least twice differentiable for this to hold.

Does ∇·(∇f × ∇g) = 0 require C² functions?

Discussion

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Does ∇·(∇f × ∇g) = 0 require C² functions?

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