A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients. (19th June 2021) - Liu, Xiong; He, Wenming
Abstract : In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form ∂ / ∂ x i a i j x / ε, x ∂ u ε x / ∂ x j = f x . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution u 0, we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution u 0 satisfies than the classical homogenization theory needs.