Boundary value problem in complex plane, how to find general solution? 
Hi
I was trying to find out general solution, can anyone explain how to find it? 

The domain is conformally equivalent to the half-plane, and hopefully you have discussed in class how to solve the Dirichlet problem in the half-plane using the Poisson kernel. Since the Laplace equation is conformally invariant it suffices to determine this conformal map. This can be done by translating the "corner" of the domain to the origin, then considering a power map: something like $z\mapsto z^{2/3}$.
