Advances in Differential Equations

Contribution to the asymptotic analysis of the Landau-de Gennes functional

Nicolas Raymond

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Abstract

In this paper, we are interested in the Landau-de Gennes functional introduced to study the transition between the smectic and nematic phases of a liquid crystal. We define a reduced functional by constraining the director field to satisfy a non-homogeneous Dirichlet condition and we prove that, below a critical temperature and if some elastic coefficients are explicitly large, the minimizers have to be nematic phases.

Article information

Source
Adv. Differential Equations Volume 15, Number 1/2 (2010), 159-180.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854767

Mathematical Reviews number (MathSciNet)
MR2588393

Zentralblatt MATH identifier
1191.35109

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx] 35Q 81Q20: Semiclassical techniques, including WKB and Maslov methods 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Citation

Raymond, Nicolas. Contribution to the asymptotic analysis of the Landau-de Gennes functional. Adv. Differential Equations 15 (2010), no. 1/2, 159--180. https://projecteuclid.org/euclid.ade/1355854767.


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