Contribution to the asymptotic analysis of the Landau-de Gennes functional

Abstract

In this paper we are interested in the Landau-de Gennes functional introduced to study the transition between the smectic and nematic phases of a liquid crystal. We define a reduced functional by constraining the director field to satisfy a non-homogeneous Dirichlet condition and we prove that, below a critical temperature and if some elastic coefficients are explicitly large, then, the minimizers have to be nematic phases.