  We will establish an $\varepsilon$-regularity result for weak solutions to
Legendre-Hadamard elliptic systems, under the a-priori assumption that the
gradient $\nabla u$ is small in $\mathrm{BMO}.$ Focusing on the case of
Euler-Lagrange systems to simplify the exposition, regularity results will be
obtained up to the boundary, and global consequences will be explored.
Extensions to general quasilinear elliptic systems and higher-order integrands
is also discussed.
