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Transforming an elliptic PDE into the Laplace equation?

  1. Apr 29, 2008 #1
    For an elliptic PDE Uxx + Uyy + Ux + Uy = -1 in D = {x^2 + y^2 = 1} and U = 0 on the boundary of D = {x^2 + y^2 = 1}
    is it possible for me to make a change of variables and eliminate the Ux and Uy and get the Laplace equation Uaa + Ubb = 0?

    I tried converting into polar coordinates, but the Ux and Uy don't seem to cancel out. Or am I approaching this the wrong way?
  2. jcsd
  3. Apr 30, 2008 #2


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    Science Advisor

    You can't get rid of the "Ux" and "Uy" by changing the independent variables but you can by letting V(x,y)= e-(1/2)(x+ y)U(x,y).
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