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Abstract
This paper concerns free elastic energy that is functional for static deformations of a nematic liquid crystal. The free elastic energy density is analysed as a non-negative quadratic form of the first-order derivatives of the director. The resulting conditions imply a system of inequalities to be held by Frank's elastic moduli, which update Ericksen's inequalities. The rejection of surface-like free elastic energy terms from bulk free elastic energy is suggested on the basis of both known and some new arguments.
Acknowledgement
This work was supported in years 2006–2008 by the Polish Ministry of Science and Higher Education under grant No N507 107 31/2555. Special thanks to Victor M. Pergamenshchik for stimulating discussion during the 22nd International Liquid Crystal Conference and to the anonymous reviewer for helpful suggestions.