AI 中文总结
该研究分析Lyuksyutov区域三维域中Landau--de Gennes泛函的全局极小元，证明其光滑收敛至$\u211d^4$值极限并得到$O(μ^{-1})$距离估计，推广了已有收敛结果。
AI 中文摘要
本文分析了Lyuksyutov区域下三维区域中Landau--de Gennes泛函的全局极小元。我们证明了其向$\u211d^4$中取值极限的光滑收敛性，并得到当$\u03bc\to +\infty$时到$\u211d^4$的距离的$O(μ^{-1})$估计，从而推广了Dipasquale等人[Arch. Ration. Mech. Anal. 239: 599--678, 2021]的收敛结果。
英文摘要
In this paper, we analyze global minimizers of the Landau--de Gennes functional in 3-dimensional domains in the Lyuksyutov regime. We prove smooth convergence to an $\mathbb{S}^4$-valued limit and obtain an $O(μ^{-1})$ estimate for the distance to $\mathbb{S}^4$ as $μ\to +\infty$, thereby extending the convergence results of Dipasquale et al.[Arch. Ration. Mech. Anal. 239: 599--678, 2021].
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