| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 47 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2025032 | |
| Published online | 04 June 2025 | |
A shape optimization problem for nematic and cholesteric liquid crystal drops
1
DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Branze 43, 25133 Brescia, Italy
2
Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy. Present address: Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, I-35121 Padova, Italy
* Corresponding author: alessandro.giacomini@unibs.it
Received:
27
August
2024
Accepted:
10
March
2025
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.
Mathematics Subject Classification: 49J45 / 26A45 / 28A75
Key words: Liquid crystals / shape optimization / sets of finite perimeter / functions of bounded variations
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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