Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

  2. jcsd
  3. Apr 16, 2010 #2


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook