A New Estimate for the Homogenization Method for Second-Order Elliptic Problem with Rapidly Oscillating Periodic Coefficients. (19th June 2021)

• Record Type: Journal Article
• Authors: Liu, Xiong; He, Wenming
• Other Names: Chen Chuanjun Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-06-19
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/8036814
• Languages: English
• ISSNs: 2314-8896

Abstract

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.