The first time in my life I have heard a boundary condition such as it is called orthogonal boundary condition for PDE. But still I might reflect a case as such: The Dirichlet BC may be defined as such that it is the analytical continuation of the solution of the problem in the interior region of PDE. That means DBC can be expressible in terms of the orthonormal set described by PDE if any? This might happen in the solution of the diffusion problem associated with the dislocation pipe diffusion in isotropic body, where the bulk diffusion occurs concurrently.