Homogenization of the Neumann boundary value problem: polygonal domains

Jie Zhao (), Juan Wang () and Jianlin Zhang ()
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Jie Zhao: Zhongyuan University of Technology
Juan Wang: Zhongyuan University of Technology
Jianlin Zhang: Zhongyuan University of Technology

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1260-1268

Abstract: 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 $$L^{p}$$ L p convergence results. Our techniques are based on using Fourier analysis method as well as Diophantine condition on the boundary

Keywords: Homogenization; Convergence rates; Polygonal domains; Diophantine condition; Primary: 35B27; Secondary: 35J15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-024-00590-8

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