Advances in Differential Equations

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

Nicolas Raymond

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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)


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

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