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Green's Function

  1. Nov 27, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm trying to show that the Green's function for the Laplace operator $-\nabla^2$ is badly behaved at infinity. I.e.

    $$\int d^dx|G(x,y)|^2=\infty$$ for d=1,2,3. What happens when d>4?

    I know the 1D Green's function is given by

    $$G(x,y)=-\frac{|x-y|}{2}$$



    2. Relevant equations



    3. The attempt at a solution

    $$G(x,y)\propto|x-y|^{-(d-2)}$$ for d>2

    I need to be able to show that the above integral diverges...
     
  2. jcsd
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