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Suppose that U_{1}is the solution of the Laplace's equation for a given set of boundary conditions and U_{2}is the the solution for the same set plus one extra boundary condition. Thus U_{2}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.

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# Uniqueness theorem for Laplace's equation

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