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Singularity in Laplacian operator

  1. Aug 12, 2012 #1
    I am trying to understand the following basic problem,

    [itex]\partial_{xx} f^\alpha (x) = \alpha (\alpha-1) \frac{1}{f^{2-\alpha}} \partial_x f + \alpha \frac{1}{f^{1-\alpha}} \partial_{xx} f [/itex]

    So it is not hard to see that if [itex] f [/itex] tends to zero the laplacian becomes undefined (im not sure if i am using proper terminology).

    that should happen for any [itex]\alpha < 2[/itex].

    I don't understand why the singulary happens and how the trivial f(x) = 0 for all x can be applied.

    thanks for the attention.
     
    Last edited: Aug 12, 2012
  2. jcsd
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