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This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in non-self-similar scales. The homogenization problem involves two oscillating scales. We obtain large-scale interior and boundary Lipschitz estimates as well as interior C 1 , α and C 2 , α estimates by utilizing higher-order correctors. We also investigate the problem of convergence rates for initial-boundary value problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, ). [ABSTRACT FROM AUTHOR]