Abstract
In this paper, we study the convergence rates for homogenization problems for solutions of partial differential equations with rapidly oscillating Neumann boundary data in the convex polygonal domains. As a consequence, we obtain the pointwise and \(L^{p}\) convergence results. Our techniques are based on using Fourier analysis method as well as Diophantine condition on the boundary
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Acknowledgements
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 Training Program for Young Backbone Teachers in Colleges and Universities of Henan Province, as well as Special Project of Basic Scientific Research Business Expenses of Zhongyuan University of Technology(K2020TD004). 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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Zhao, J., Wang, J. & Zhang, J. Homogenization of the Neumann boundary value problem: polygonal domains. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00590-8
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DOI: https://doi.org/10.1007/s13226-024-00590-8