Regularity and Behavior of Eigenvalues for Minimizers of a Constrained Q-Tensor Energy for Liquid Crystals

We investigate minimizers defined on a bounded domain for the Maier-Saupe energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model, so as to constrain the competing states to take values in the closure of a physically realistic range. We prove that minimizers are regular and in several model problems we are able to use this regularity to prove that minimizers take on values strictly within the physical range.Non UBCUnreviewedAuthor affiliation: Purdue UniversityFacult