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Dirichlet Problem on a Disc - Transfomation

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data

    This is a problem I found in my note. It says that from u xx(subscript) + u yy = 0, we can arrive at u rr + (1/r) u r + (1/r^2) u theta theta = 0 by using the transformation x = r cos theta, y = r sin theta, r = square root of (x^2+y^2), theta = arctan (y/x).

    The problem is how to prove it?


    2. Relevant equations

    The strategy is to express u xx and u yy in terms of u rr , u r theta and u theta theta.


    3. The attempt at a solution

    I can differentiate r with respect to x an y. Also, I have found the derivative of theta with respect to x and y.

    I have no problem of finding u x and u y. The problems arise when I try to find u xx and u yy. ;(

    I use the search engine to search for the proof but can't find it anywhere. Does someone have the link for this proof? Thanks.
     
  2. jcsd
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