Refinement of boundary conditions for nematic liquid crystals in the one-constant approximation

The boundary conditions are studied for a nematic liquid crystal in the case of weak anchoring. The cases of the general expression and one-constant approximation are considered for the Frank energy. It is shown that the one-constant approximation is correct for one-dimensional problems only and, for two- and three-dimensional problems, this model significantly simplifies the boundary conditions and changes their type.