Variational models for nematic liquid crystals with subquadratic growth
Nematic liquid crystals are matter in an intermediate phase between the solid and the liquid ones. Materials in the nematic phase may have topological defects, that is, regions of sharp optical contrast that carry topological invariants. In this talk, we will briefly discuss the mathematical modelling of nematic liquid crystals and their defects. In particular, we will focus on some variational continuum models with subquadratic growth in the gradient. The talk is based on joint works with Apala Majumdar (University of Bath, UK), Giandomenico Orlandi (University of Verona, Italy), and Bianca Stroffolini (University of Naples Federico II, Italy).