Finding a Function H in C to Satisfy Conditions

libelec
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Homework Statement



Find a function H in C such that {\nabla ^2}H = 0 for y>0, H(0,y) = 1 for y<-/pi, H(0,y) = 0 for y>/pi and H(0,y) = -1 for -/pi<y</pi.

The Attempt at a Solution



I haven't been able to came up with anything. All the conform transformations that I know allow me to solve the Dirichlet problem with only 2 conditions, or 3 but with two of them with the same value. I was told that I could just leave the geometry of the problem like it is (that is, not make any transformation) and propose the solution A\theta1 + B\theta2 + C, being \theta1 the argument of [z - (0 -i*Pi)] and \theta2 the argument of [z - (0 +i*Pi)], but the solution I find doesn't satisfy the border conditions.

Any ideas?
 
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