Abstract
In this paper, we investigate the structure of local minimizers for the isotropic–nematic interface based on the Landau-de Gennes energy. In the absence of the anisotropic energy, the uniaxial solution is the only local minimizer in 1-D. In 3-D, we propose a De Giorgi’s type conjecture and give an affirmative answer under a mild assumption. In the presence of the anisotropic energy with \(L_2>-\,1\) and homeotropic anchoring, the uniaxial solution is also the only local minimizer in a class of diagonal form in 1-D.
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Acknowledgements
P. Zhang is partially supported by NSF of China under Grant 11421101 and 11421110001. Z. Zhang is partially supported by NSF of China under Grants 11371039 and 11425103.
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Communicated by F. H. Lin.
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Chen, J., Zhang, P. & Zhang, Z. Local minimizer and De Giorgi’s type conjecture for the isotropic–nematic interface problem. Calc. Var. 57, 129 (2018). https://doi.org/10.1007/s00526-018-1404-0
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DOI: https://doi.org/10.1007/s00526-018-1404-0