Take the 2-minute tour ×  Does the Laplace equation on a
rectangle with Dirichlet boundary conditions at two opposing
sides and Neumann boundary conditions at the other two, always
have a solution? If it does, is it unique? Is the same true for
the discrete Laplace equation (with the standard five-point
laplacian)?  share|improve this question  3 Answers 3  The
solution to the Dirichlet problem is unique by the maximum
principle. For the same reason, the solution to the Neumann
problem is unique up to a constant.  At worst your problem would
fail uniqueness by a constant, but those Dirichlet conditions
you've got will prevent this.  This carries over to the discrete
case. But note that the discrete case is an easier problem since
you can just write out the matrix you need to invert and check
if it's invertible.  share|improve this answer  I am not
familiar with the discrete case. As for continuous case, I think
you can use the method of images to solve this problem. It
should always have a solution and it sho