Various results concerning homogenisation of nematic liquid crystals

Resumen

In this tesis we present various results concerning homogenisation ofnematic liquid crystals: two of them are in perforated domains, while the other oneconcerns rates of convergence for boundary homogenisation. The first workdescribed in this thesis is a convergence result for the Landau-de Gennes model in3D domains with connected perforations. The goal of the analysis is to find newterms in the energy functional that are independent of the gradient. The secondresult is an error estimate for a 2D toy model used to describe rugosity effects innematic liquid crystals via homogenisation problems, using once again the LandaudeGennes model. The last problem is a local L2-convergence result for ahomogenisation problem in with isolated perforations. Here we use the Oseen-Frank model, with the goal of finding new gradient-dependent terms in the energyfunctional.