On ^{L p} estimates in homogenization of elliptic equations of maxwell's type

For a family of second-order elliptic systems of Maxwell's type with rapidly oscillating periodic coefficients in a ^C1,α domain Ω, we establish uniform estimates of solutions _uε and ∇; × _uε in ^{L p}(Ω) for 1 < p ≤ ∞ The proof relies on the uniform ^W1,p and Lipschitz estimates for solutions of scalar elliptic equations with periodic coefficients.