Hello all. I am working on a problem and I am getting a bit confused. Suppose we have a poisson equation that we wish to solve subject to certain boundary conditions. Let's say we are in 1D (we can later extrapolate to more dimensions). Is it possible to impose Dirichlet boundary conditions on the boundary, but also specify a known derivative of the function in a certain region? In a physical context, I want to solve poisson's eq but want to specifiy the potential at the boundary and set the field to zero in a certain region. Will this overconstrain the system? Thanks and please let me know if this is unclear.