A shape optimization problem for nematic and cholesteric liquid crystal drops
Analysis of PDEs
2024-08-29 v2
Abstract
We generalize the shape optimization problem for the existence of stable equilibrium configurations of nematic and cholesteric liquid crystal drops surrounded by an isotropic solution to include a broader family of admissible domains with inner boundaries, allowing discontinuities in the director field across them. Within this setting, we prove the existence of optimal configurations under a volume constraint and show that the minimization problem is a natural generalization of that posed for regular domains.
Cite
@article{arxiv.2408.05651,
title = {A shape optimization problem for nematic and cholesteric liquid crystal drops},
author = {Alessandro Giacomini and Silvia Paparini},
journal= {arXiv preprint arXiv:2408.05651},
year = {2024}
}
Comments
Keywords: Liquid crystals, shape optimization, sets of finite perimeter, functions of bounded variations