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Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation

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Summary

We prove existence of minimizers of the functional\(\int\limits_\Omega {\left( {\kappa \left| {\nabla s} \right|^2 + s^2 \left| {\nabla u} \right|^2 + \Psi (s)} \right)} {\mathbf{ }}dx\) recently suggested by Ericksen [8] for the statics of nematic liquid crystals. A set of necessary conditions for the minimizers and a monotonicity formula are also found.

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  1. Dipartimento di Matematica, II Università di Roma, Tor Vergata, Roma

    Luigi Ambrosio

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  1. Luigi Ambrosio
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Ambrosio, L. Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation. Manuscripta Math 68, 215–228 (1990). https://doi.org/10.1007/BF02568761

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  • DOI: https://doi.org/10.1007/BF02568761

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