Regularity and the behavior of eigenvalues for minimizers of a constrained Q-tensor energy for liquid crystals
Regularity and the behavior of eigenvalues for minimizers of a constrained Q-tensor energy for liquid crystals
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DOI：
10.1007/s00526-016-1009-4
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发表时间：
2015-11
影响因子：
2.1
通讯作者：
P. Bauman;D. Phillips
中科院分区：
文献类型：
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作者：
P. Bauman;D. Phillips
本文研究了Maier-Saupe Q-张量能量在有界域上定义的极小化子。能量密度是奇异的，如鲍尔和马宗达对朗道-德热内斯Q张量模型的修改，以限制竞争态在物理上现实的范围内具有本征值。我们证明了极小化是正规的，在几个模型问题中，我们能够使用这种规律性来证明极小化具有严格的物理范围内的特征值。
We investigate minimizers defined on a bounded domain infor the Maier–Saupe Q-tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Majumdar’s modification of the Landau-de Gennes Q-tensor model, so as to constrain the competing states to have eigenvalues in the closure of a physically realistic range. We prove that minimizers are regular and in several model problems we are able to use this regularity to prove that minimizers have eigenvalues strictly within the physical range.