I need some help solving a Dirichlet problem using a conformal map I'm struggling here, trying to understand how to do this, and after 4 hours of reading, i still can't get around the concept and how to use it.
Basically, i have this problem:
A={(x,y) / x≥0, 0≤y≤pi
So U(x,0) = B; U(x,pi) = C; U'x(0,y) = 0;
I know that inside A, the laplace operator of U is 0. So i have to find U, and U must meet those requirements.
I don't have to use any form of differential equation. I'm supposed to find some sort of conformal transformation in order to make the domain a little more.. easy to understand. And then i should just get a result.
The problem is, i think i don't know how to do that. If any of you could help me understand how to solve this one, i might get the main idea and i could try to reproduce the resolution in similar cases.
Thank you very much, and i'm sorry for my english.

The domain is simple enough already. Observe that there is a function of the form $U=\alpha y+\beta$ which satisfies the given conditions. 
