Uniform boundary estimates in homogenization of higher-order elliptic systems.

This paper focuses on uniform boundary estimates in homogenization of a family of higher-order elliptic operators Lε, with rapidly oscillating periodic coefficients. We derive uniform boundary Cm-1,λ(0<λ<1) and Wm,p estimates in C1 domains, as well as uniform boundary Cm-1,1 estimate in C1,θ(0<θ<1) domains without the symmetry assumption on the operator. The proof, motivated by the works "Armstrong and Smart in Ann Sci Éc Norm Supér (4) 49(2):423-481 (2016) and Shen in Anal PDE 8(7):1565-1601 (2015)," is based on a suboptimal convergence rate in Hm-1(Ω). Compared to "Kenig et al. in Arch Ration Mech Anal 203(3):1009-1036 (2012) and Shen (2015)," the convergence rate obtained here does not require the symmetry assumption on the operator, nor additional assumptions on the regularity of u0 (the solution to the homogenized problem), and thus might be of some independent interests even for second-order elliptic systems. [ABSTRACT FROM AUTHOR]