Solve the boundary value problem:
$$Δu=f(r), 0<r<R, 0\leq θ\leq2 π,$$ $$u(R,θ)=g(θ), 0\leq θ\leq2 π.$$
Where $Δu$ denote $u_{rr}+\frac{1}{r}u_r+\frac{1}{r^2}u_{θθ}$ and $R$ is a fix value. I know how to solve this problem when $f(r)=0$ or when $g(θ)=0$, but in this case I can't find the answer.
Anyone can help me please?.