On minimizers for the isotropic-nematic interface problem

In this paper, we investigate the structure and stability of the isotropic- nematic interface in 1-D. In the absence of the anisotropic energy, the uniaxial solution is the only global minimizer. In the presence of the anisotropic energy, the uniaxial solution with the homeotropic anchoring is stable for L-2 < 0 and unstable for L-2 > 0. We also present many interesting open questions, some of which are related to De Giorgi conjecture.A3 Foresight Program among China (NSF); Japan (JSPS); Japan Korea [NRF 2014K2A2A6000567]; China Postdoctoral Science Foundation [2013M540010, 2014T70008]; NSF of China [11501502, 11421101, 11421110001, 11371039, 11425103]SCI(E)ARTICLE25