具有任意正展曲、扭曲和弯曲常数的Oseen-Frank极小化子的边界正则性
Boundary regularity for Oseen-Frank minimizers with arbitrary positive splay, twist, and bend constants
AI总结：
针对Oseen-Frank能量的全局极小化子，在无小各向异性假设下证明其边界正则性，解决了Lin和Liu问题(c)的边界正则性部分。
AI中文摘要：
设Ω⊂ℝ³为光滑有界域，g:∂Ω→𝕊²为光滑映射。我们证明，在满足强锚定条件n=g时，Oseen-Frank能量的任意全局极小化子在∂Ω的完整邻域内是光滑的。该结果适用于任意正的展曲、扭曲和弯曲常数，无需任何小各向异性假设，解决了Lin和Liu提出的纯Oseen-Frank问题及其给定光滑磁场扰动下的问题(c)的边界正则性部分。
英文摘要：
Let $Ω\subset\mathbb R^3$ be a smooth bounded domain and let $g:\partialΩ\to\mathbb S^2$ be smooth. We prove that any global minimizer of the Oseen--Frank energy subject to the strong anchoring condition $n=g$ is smooth in a full neighborhood of $\partialΩ$. The result holds for arbitrary positive splay, twist, and bend constants, without any small-anisotropy assumption. It resolves the boundary-regularity part of Lin and Liu's Problem~(c) for the pure Oseen--Frank problem and for its prescribed smooth magnetic-field perturbation.
