Abstract
In this paper, we mainly employed the idea of the previous paper [34] to study the sharp uniform W1,p estimates with 1<p≤∞ for more general elliptic systems with the Neumann boundary condition on a bounded C1,η domain, arising in homogenization theory. Based on the skills developed by Z. Shen in [27] and by T. Suslina in [31,32], we also established the L2 convergence rates on a bounded C1,1 domain and a Lipschitz domain, respectively. Here we found a “rough” version of the first order correctors (see (1.12)), which can unify the proof in [27] and [32]. It allows us to skip the corresponding convergence results on Rd that are the preconditions in [31,32]. Our results can be regarded as an extension of [23] developed by C. Kenig, F. Lin, Z. Shen, as well as of [32] investigated by T. Suslina.
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