Homogenization of elliptic systems with stratified structure revisited. Issue 7 (2nd July 2020)

• Record Type: Journal Article
• Authors: Xu, Yao; Niu, Weisheng
• Is Part Of: Communications in partial differential equations. Volume 45:Issue 7(2020)
• Page Start: 655
• Page End: 689
• Publication Date: 2020-07-02
• Subjects: Convergence rates -- elliptic systems -- periodic homogenization; 35B27; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2019.1709871
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We consider quantitative estimates in periodic homogenization for second-order elliptic systems with stratified structure on bounded Lipschitz domains. Under rather general smoothness assumptions on A and ρ, we establish a sharp-order scale-invariant convergence rate in L 2 d / ( d − 1 ) ( Ω ) . As a byproduct, a qualitative homogenization result is also derived under more or less sharp conditions on A and ρ . The results obtained here improve our previous results greatly.