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For a family of second-order parabolic systems with bounded measurable, rapidly oscillating and time-dependent periodic coefficients, we investigate the sharp convergence rates of weak solutions in L 2 . Both initial-Dirichlet and initial-Neumann problems are studied. [ABSTRACT FROM AUTHOR]

Abstract: Let be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform estimate in a Lipschitz domain Ω in for solutions to the Dirichlet problem: in Ω and on ∂Ω, where and C, are constants independent of . The ranges are sharp for or 3. [Copyright &y& Elsevier]

Abstract: We show that the Neumann problem for Laplace''s equation in a convex domain Ω with boundary data in is uniquely solvable for . As a consequence, we obtain the Helmholtz decomposition of vector fields in . [Copyright &y& Elsevier]