Boundary regularity for Oseen-Frank minimizers with arbitrary positive splay, twist, and bend constants

Let $\mathrm{\Omega }\subset {\mathbb{R}}^3$ be a smooth bounded domain and let $g:\mathrm{\partial }\mathrm{\Omega }\to {\mathbb{S}}^2$ 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 $\mathrm{\partial }\mathrm{\Omega }$. 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~© for the pure Oseen–Frank problem and for its prescribed smooth magnetic-field perturbation.