Does the following PDE with local boundary condition have a unique solution:
\begin{cases} \hfill \Delta u=0 \hfill & \Omega \\ \hfill \frac{\partial u}{\partial n_+}- \frac{\partial u}{\partial n_-}=u\hfill & \partial\Omega, \\ \end{cases} where $\frac{\partial }{\partial n_+}$ and $\frac{\partial }{\partial n_-}$ are the exterior and interior normal derivatives.