Abstract
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.
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Acknowledgements
We would like to thank the anonymous referee for the careful reading and very useful comments. Part of this paper was carried out while the first author was visiting Peking University and the second author was visiting NYU Shanghai and Chungnam National University. The first author gratefully acknowledges hospitality of Peking University during his visit and the second author also wishes to thank NYU-Shanghai and Chungnam National University for the warm hospitality. J. Park’s work is partially supported by A3 Foresight Program among China (NSF), Japan (JSPS), and Korea (NRF 2014K2A2A6000567). W. Wang’s work is partially supported by China Postdoctoral Science Foundation under Grant 2013M540010 and 2014T70008, and NSF of China under Grant 11501502. P. Zhang’s work is partially supported by NSF of China under Grant 11421101 and 11421110001 and the work of Z. Zhang is partially supported by NSF of China under Grant 11371039 and 11425103.
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Communicated by F. H. Lin.
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Park, J., Wang, W., Zhang, P. et al. On minimizers for the isotropic–nematic interface problem. Calc. Var. 56, 41 (2017). https://doi.org/10.1007/s00526-017-1131-y
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DOI: https://doi.org/10.1007/s00526-017-1131-y