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arXiv · 1804.10739

First-order expansions for eigenvalues and eigenfunctions in periodic homogenization

Jinping Zhuge
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Abstract

For a family of elliptic operators with periodically oscillating coefficients, $-\text{div}( A(\cdot/\varepsilon) \nabla) $ with tiny $\varepsilon>0$, 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 $L^2$ or $H^1_{\text{loc}}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

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Jinping Zhuge. 2018-04-28. First-order expansions for eigenvalues and eigenfunctions in periodic homogenization. https://arxiv.org/abs/1804.10739

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