We consider the existence and regularity of a weak solution to a class of systems containing a p-curl system in a multi-connected domain. This paper extends the result of the regularity theory for a class containing a...We consider the existence and regularity of a weak solution to a class of systems containing a p-curl system in a multi-connected domain. This paper extends the result of the regularity theory for a class containing a p-curl system that is given in the author's previous paper. The optimal C^1+a-regularity of a weak solution is shown in a multi-connected domain.展开更多
We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values Hn and Hsh of applied magnetic...We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values Hn and Hsh of applied magnetic field. When the intensity of the magnetic field is smaller than Hn, the configuration of the energy is only global minimizer, when the intensity is between Hn and Hsh, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.展开更多
文摘We consider the existence and regularity of a weak solution to a class of systems containing a p-curl system in a multi-connected domain. This paper extends the result of the regularity theory for a class containing a p-curl system that is given in the author's previous paper. The optimal C^1+a-regularity of a weak solution is shown in a multi-connected domain.
文摘We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values Hn and Hsh of applied magnetic field. When the intensity of the magnetic field is smaller than Hn, the configuration of the energy is only global minimizer, when the intensity is between Hn and Hsh, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.
