Professor of Mathematics
Department of Mathematics
We investigate minimizers defined on a two-dimensional domain for the Maier--Saupe energy used to characterize nematic liquid crystal configurations. The energy density for the model is singular so as to constrain the competing states to take on physical values. We prove that minimizers are regular and in certain cases we are able to use this regularity to prove that minimizers must take on values strictly within the physical regime. This work is joint with Patricia Bauman.