CONVERGENCE RATES FOR GENERAL ELLIPTIC HOMOGENIZATION PROBLEMS IN LIPSCHITZ DOMAINS.

The paper extends the results obtained by Kenig, Lin, and Shen [Arch. Ration. Mech. Anal., 203 (2012), pp. 1009--1036] to more general elliptic homogenization problems in two perspectives: lower order terms in the operator and no smoothness on th e coefficients. We do not repeat their arguments. Instead we find the new weighted-type estimates for the smoothing operator at scale e, and combining some techniques developed by Shen in [preprint, arXiv:1505.00694v1, 2015] leads to our main results. In addition, we also obtain sharp O(ε) convergence rates in Lp with p = 2d/(d - 1), which were originally established by Shen for elasticity systems in [preprint, arXiv:1505.00694v1, 2015]. Also, this work may be regarded as the extension of [T. Suslina, Mathematika, 59 (2013), pp. 463-476; T. Suslina SIAM J. Math. Anal, 45 (2013), pp. 3453-3493] developed by Suslina concerned with the bounded Lipschitz domain. [ABSTRACT FROM AUTHOR]