Abstract
In this paper, we study reiterated homogenization problems for equations −div(A(x/ε, x/ε2)∇uε) = f (x). We introduce auxiliary functions and obtain the representation formula satisfied by uε and homogenized solution u0. Then we utilize this formula in combination with the asymptotic estimates of Neumann functions for operators and uniform regularity estimates of solutions to obtain convergence rates in Lp for solutions as well as gradient error estimates for Neumann problems.
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Acknowledgement
The author would like to thank the reviewers for their valuable comments and helpful suggestions to improve the quality of this paper. This work has been supported by Natural Science Foundation of China (No. 11626239), China Scholarship Council (No. 201708410483), as well as Foundation of Education Department of Henan Province (No. 18A110037). The part of this work was done while the author was visiting School of Mathematics and Applied Statistics, University of Wollongong, Australia.
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Wang, J., Zhao, J. Convergence Rates of Solutions for Elliptic Reiterated Homogenization Problems. Indian J Pure Appl Math 51, 839–856 (2020). https://doi.org/10.1007/s13226-020-0435-3
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DOI: https://doi.org/10.1007/s13226-020-0435-3