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Question about Identity

  1. Jan 21, 2016 #1
    Hey all,
    As I was working on my numerical PDEs homework, an identity came up which we used to solve a problem. I was able to answer the question, but my question here is where does the identity come from (I figured it has something to do with analysis) ?

    The identity is
    The integral of $$v^2$$ over some region D is equivalent to the integral of $$v^2\Delta \phi$$ over D, where $$\phi = \frac{1}{2d}|x|^2$$

    I haven't taken an analysis class so not too sure where this comes from
  2. jcsd
  3. Jan 21, 2016 #2


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    I don't understand this.
  4. Jan 21, 2016 #3
    The reqs for the class are the standard calc/DE/lin. alg sequence, and I've also taken the PDE theory class so I thought it was worth a shot. I've been managing to learn the basic aspects of analysis and some of the major theorems along the way, but just not too sure where the identity comes from
  5. Jan 21, 2016 #4
    Actually, I think I figured it out. Abs(x) is just r, and the laplacian of r^2 is just a constant (2d), so that laplacian of phi is one, and hence the identity
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