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

Green's function in n-dim, but with one independent variable.

  1. Jul 21, 2014 #1
    Suppose we have some partial differential equation for a scalar ##f##
    $$Df = \rho$$
    taking values in ##\mathbb{R}^n##, and further suppose that the differential equation is completely independent of the variable ##y:=x^n## so that the differential operator ##D## only contains derivatives with respect to ##x^1,\ldots, x^{n-1}##, and ##f## as well as ##\rho## is also independent of ##x^n##. Would it then be correct to use a Green's function

    $$D G(\vec r- \vec r') = \delta^{(n-1)}(\vec r - \vec r')$$
    for ##\vec r, \vec r' \in \mathbb{R}^{n-1}## and with
    $$f(\vec r) = \int_{\mathbb{R}^{n-1}} d^{n-1} \vec r' G(\vec r - \vec r') \rho(\vec r')$$?

    In other words, would it be correct to just use the method of greens functions in ##n-1## dimensions, and pretend that the ##n##'th dimension is not there?
     
  2. jcsd
  3. Aug 5, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Green's function in n-dim, but with one independent variable.
  1. Green's function (Replies: 6)

  2. Green functions (Replies: 3)

Loading...