First-order expansions for eigenvalues and eigenfunctions in periodic homogenization. Issue 5 (October 2020)

• Record Type: Journal Article
• Authors: Zhuge, Jinping
• Is Part Of: Proceedings. Volume 150:Issue 5(2020)
• Page Start: 2189
• Page End: 2215
• Publication Date: 2020-10
• Subjects: Homogenization, -- eigenvalues, -- eigenfunctions, -- boundary layers; 35B27, -- 35P20; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2019.8
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract: For a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L 2 or $H^1_{\rm loc}$ . Our results rely on the recent progress on the homogenization of boundary layer problems.