Is there any "second order Neumann condition"? i.e. I mean $\frac{\partial^2 f}{\partial \vec{n}^2} = g$
I think $\frac{\partial^2 f}{\partial \vec{n}^2}$ can be defined as $\triangledown( \triangledown f) \cdot \vec{n} $, right?
If we don't usually do this, may I know why? What difficulties will occur in this boundary condition?