Hi all. Suppose that U1 is the solution of the Laplace's equation for a given set of boundary conditions and U2 is the the solution for the same set plus one extra boundary condition. Thus U2 satisfies the Laplace's equation and the boundary conditions of the first problem, so it's a solution of the first problem. I know that the above argument must be wrong according to the uniqueness theorem, but what's wrong with it? Thanks in advance.