On the Landau-de Gennes elastic energy of constrained biaxial nematics (Q2811887)

The Landau-de Gennes theory is a model in which a nematic liquid crystal is described by a tensor order parameter which is a symmetric traceless \(3^2\) matrix. This Landau-de Gennes model involves the free energy function of the nematic crystal which can be represented as the sum of the bulk free-energy on the one hand, and the elastic part of the energy on the other hand; and a question of interest is whether the elastic energy can be a coercived function. The paper is centered on the fact that, in effect, it may be coercive under some conditions. The proof of this main result is accompanied with some side results. The coercivity of the energy is of importance and of interest as far as it is related with stability.