I am very confused. So I have Laplace's equation $\nabla^2\phi(x,y)=0$
and B.C.'s $\phi(x,0)=f(x); \,\,\,\,\,\, \phi(x,1)\equiv0$ where
I have to solve it by Fourier transform.
So I take the Fourier transform of the equation $-k^2\Phi(k,y)=0$ But I don't expect $\Phi$ to be identically $0$...?
Also, I have no idea how to proceed and it's driving me nuts. PLease help! Thanks.