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

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We impose the strong anchoring condition, and we allow the boundary data to be nonconstant and also the applied field to be nonconstant. Thus, we shall extend the results of Lin and Pan in 2007. We show that for some specific configuration there exist 2 critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only a global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not a global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration 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 infinity.