arXiv:2412.13824 Abstract | arXiv Analytics

arXiv:2412.13824 [math.AP]Abstract References Reviews Resources

Lipschitz regularity of homogenization with continuous coefficients: Dirichlet problem

Published 2024-12-18Version 1

We study uniform Lipschitz regularity estimates for elliptic systems in divergence form with continuous coefficients, based on rapidly oscillating periodic coefficients derived from homogenization theory. We extend a result by Avellaneda and Lin [Comm. Pure Appl. Math. 40 (1987), pp. 803-847] by minimizing all regularity conditions of the given data to integral conditions. We remark that the coefficients of an elliptic operator have Dini mean oscillation, which corresponds to the results of the latest general regularity theory.

Categories: math.AP

Keywords: continuous coefficients, dirichlet problem, homogenization, study uniform lipschitz regularity estimates, oscillating periodic coefficients

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