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Vector identity

  1. Apr 16, 2010 #1
    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!
     
  2. jcsd
  3. Apr 16, 2010 #2

    phyzguy

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    Science Advisor

    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.
     
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