BMO varepsilon -regularity results for solutions to Legendre–Hadamard elliptic systems

Abstract

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 textrm{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.