Shen, Zhongwei; Zhuge, Jinping Approximate correctors and convergence rates in almost-periodic homogenization. (English) Zbl 1409.35027 J. Math. Pures Appl. (9) 110, 187-238 (2018). The aim of this study is the quantitative homogenization of second-order elliptic equations with bounded measurable coefficients which are almost-periodic in the sense of Weyl/Besicovitch. The target equation is posed in an “homogeneous” domain. Uniform local \(L^2\) estimates for approximate correctors are obtained in terms of a function that quantifies the almost-periodicity of the coefficient matrix. Furthermore, a condition that implies the existence of correctors is given. Reviewer: Adrian Muntean (Karlstad) Cited in 13 Documents MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74Q20 Bounds on effective properties in solid mechanics 35J25 Boundary value problems for second-order elliptic equations 35B15 Almost and pseudo-almost periodic solutions to PDEs Keywords:quantitative homogenization PDFBibTeX XMLCite \textit{Z. Shen} and \textit{J. Zhuge}, J. Math. Pures Appl. (9) 110, 187--238 (2018; Zbl 1409.35027) Full Text: DOI arXiv References: [1] Kozlov, S., Averaging differential operators with almost periodic, rapidly oscillating coefficients, Math. USSR Sb., 35, 481-498 (1979) · Zbl 0422.35003 [2] Papanicolaou, G.; Varadhan, S., Boundary value problems with rapidly oscillating random coefficients, (Proceed. Colloq. on Random Fields, Rigorous Results in Statistical Mechanics and Quantum Field Theory. Proceed. Colloq. on Random Fields, Rigorous Results in Statistical Mechanics and Quantum Field Theory, Colloq. Math. 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