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Conformal and non-conformal transformations

  1. Nov 26, 2015 #1
    It is well known that from a two-dimensional solution of Laplace equation for a particular geometry, other solutions for other geometries can be obtained by making conformal transformations.

    Now, I have a function defined on a disc centered at the origin and is given by

    f(r) = a r

    where a is constant and r is the radial distance from the origin. My function is obviously not a solution of the Laplace equation. However, I want to see if it is possible to find a transformation (conformal or non-conformal) that maps this to a rectangle (centered on the origin with length L in the x-direction and width W in the y-direction) so that I obtain the corresponding solution on the rectangular geometry similar to what is done with Laplace solutions.
  2. jcsd
  3. Nov 29, 2015 #2


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    Science Advisor
    Gold Member

    Only analytic functions have conformal maps, so your first step is to determine whether your function is analytic over the disk.
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