Homogenization for both oscillating operator and Neumann boundary value: $$W^{1,p}$$ W 1, p convergence rate

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

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 876-882

Abstract: Abstract In this paper, we will study the $$W^{1,p}$$ W 1 , p convergence rate for homogenization problems of solutions for both oscillating operator and Neumann boundary data. By introducing the auxiliary periodic problems as well as Neumann correctors, we reduce the setting of both oscillating operator and Neumann boundary data to a fixed operator, which utilize mostly the fact that the Neumann function as well as its gradient pointwise convergence results, respectively. Boundary layer phenomena in periodic homogenization is also considered.

Keywords: Homogenization; Convergence rates; Oscillating; Neumann functions; Primary: 35B27; Secondary: 35J15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00305-x

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