Regularity estimates for higher order elliptic systems on Reifenberg flat domains

Consider a higher order elliptic system

for all i=1,…,N with N∈N₊, and all multi-indices |α|=m_i, |β|=m_j with m_i∈N₊ for all i=1,…,N, and the standard summation notation is understood. We assume that the leading coefficients  have small BMO norms and the domain Ω⊂Rn is open, bounded and flat in the Reifenberg's sense. This article is to prove the regularity estimates of this system in weighted Lorentz spaces and in Lorentz–Morrey spaces. Our results require weak assumptions on the regularity of the coefficients  and the boundary ∂Ω, and they are new even for scalar higher order elliptic equations