$\mathrm{B}\mathrm{M}\mathrm{O}$ $\epsilon$-regularity results for solutions to Legendre-Hadamard elliptic systems

We will establish an $\epsilon$-regularity result for weak solutions to Legendre-Hadamard elliptic systems, under the a-priori assumption that the gradient $\mathrm{\nabla }u$ is small in $\mathrm{B}\mathrm{M}\mathrm{O}\mathrm{.}$ 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.