A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients - Xiong Liu; Wenming He (Journal of Function Spaces)
In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂/∂xiaijx/ε,x∂uεx/∂xj=fx. Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u0, we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u0 satisfies than the classical homogenization theory needs.