  In this note we study the boundary regularity of minimizers of a family of
weak anchoring energies that model the states of liquid crystals. We establish
optimal boundary regularity in all dimensions $n\geq 3 .$ In dimension $n=3,$
this yields full regularity at the boundary which stands in sharp contrast with
the observation of boundary defects in physics works. We also show that, in the
cases of weak and strong anchoring, regularity of minimizers is inherited from
that of their corresponding limit problems.The analysis rests in a crucial
manner on the fact that the surface and Dirichlet energies scale differently;
we take advantage of this fact to reduce the problem to the known regularity of
tangent maps with zero Neumann conditions.
