First-order expansions for eigenvalues and eigenfunctions in periodic homogenization

2018/04/28 by Jinping Zhuge, Zhuge, Jinping
Computer Science · Engineering · #35B27 #35P20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1804.10739

openalex publication_date 2018/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a family of elliptic operators with periodically oscillating coefficients, -div( A(⋅/ε) ∇) with tiny ε>0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both 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 L² or H¹_loc. Our results rely on the recent progress on the homogenization of boundary layer problems.

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