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I am wondering if the below problem is solvable or not. Laplace equation between two circle with raduses equal to $r=1$ and $r=r_0$ where $r_0<1$:

$\nabla^2 \phi(r,\theta)=0$

The boundary conditions are:

$\phi(r=1,\theta)=\theta_1+\left\{ \begin{array}{ll} \pi/4 & 0<\theta<\pi \\ -\pi/4 & \pi<\theta<2\pi \end{array} \right.$

$\phi(r=r_0,\theta)=\theta_2+\left\{ \begin{array}{ll} -\pi/4 & 0<\theta<\pi \\ \pi/4 & \pi<\theta<2\pi \end{array} \right.$

$\theta_1$ and $\theta_2$ are constants.

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