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## Main Question or Discussion Point

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?

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?