Convergence Rates of Solutions for Elliptic Reiterated Homogenization Problems

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

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 839-856

Abstract: 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.

Keywords: Reiterated homogenization; convergence rates; Neumann functions; regularity estimate; 35B27; 35J15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0435-3

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