Abstract
The paper is devoted to the homogenization of elliptic systems in divergence form. We obtain uniform interior as well as boundary Lipschitz estimates in a bounded C1, γ domain when the coefficients are Dini continuous, inhomogeneous terms are divergence of Dini continuous functions and the boundary functions have Dini continuous derivatives. The results extend Avellaneda and Lin’s work [Comm. Pure Appl. Math., 40: 803–847 (1987)], where H¨older continuity is the main assumption on smoothness of the data.
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Supported in part by the National Natural Science Foundation of China (No.12071365 and 12001419).
Without loss of generality, we assume that \({\omega _a}\left(r \right) \ge {r^{{\gamma \over 2}}}\) as r > 0. Observe C1, γ is the smoothness of Ω.
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Dong, R., Li, Ds. & Zhang, Hl. Uniform Lipschitz Estimates of Homogenization of Elliptic Systems in Divergence Form with Dini Conditions. Acta Math. Appl. Sin. Engl. Ser. 37, 48–68 (2021). https://doi.org/10.1007/s10255-021-1001-4
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DOI: https://doi.org/10.1007/s10255-021-1001-4