Gradient theory of domain walls in thin, nematic liquid crystals films

In this paper we describe domain walls appearing in a thin, nematic liquid crystal sample subject to an external field with intensity close to the Fr\'eedericksz transition threshold. Using the gradient theory of the phase transition adopted to this situation, we show that depending on the parameters of the system, domain walls occur in the bistable region or at the border between the bistable and the monostable region.