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We consider the stability of a specic nematic liquid crystal conguration under an applied magnetic eld. We impose the strong anchoring condition, and we allow the boundary data to be nonconstant and also the applied eld to be nonconstant. Thus, we shall extend the results of Lin and Pan in 2007. We show that for some specic conguration there exist 2 critical values Hn and Hsh of applied magnetic eld. When the intensity of the magnetic eld is smaller than Hn, the conguration of the energy is only a global minimizer, when the intensity is between Hn and Hsh, the conguration is not a global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the conguration is not weakly stable. Moreover, we also examine the behavior of minimal values of energy and the asymptotic behavior of the global minimizer as the intensity tends to innity. eld-induced stability, variational problem, nematic liquid crystal

Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals