First-order expansions for eigenvalues and eigenfunctions in periodic homogenization
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, s...
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| Vydáno v: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Ročník 150; číslo 5; s. 2189 - 2215 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Edinburgh, UK
Royal Society of Edinburgh Scotland Foundation
01.10.2020
Cambridge University Press |
| Témata: | |
| ISSN: | 0308-2105, 1473-7124 |
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| 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 L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems. |
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| AbstractList | 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 L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems. 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. |
| Author | Zhuge, Jinping |
| Author_xml | – sequence: 1 givenname: Jinping surname: Zhuge fullname: Zhuge, Jinping email: jinping.zhuge@uky.edu organization: Department of Mathematics, University of Kentucky, Lexington, KY40506, USA (jinping.zhuge@uky.edu) |
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| Cites_doi | 10.1007/s11511-012-0083-5 10.1080/03605302.2018.1446160 10.1017/S0308210500027050 10.4171/JEMS/286 10.1007/978-3-319-91214-1 10.1007/BF01442554 10.3233/ASY-121158 10.1007/s00205-017-1142-z 10.1016/S0021-7824(98)80068-8 10.1137/0153076 10.1090/S0025-5718-1975-0383117-3 10.1002/cpa.21740 10.1007/BF01442551 10.4171/JEMS/408 |
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| References | S0308210519000088_ref15 S0308210519000088_ref13 S0308210519000088_ref6 Allaire (S0308210519000088_ref1) 1998; 77 S0308210519000088_ref7 S0308210519000088_ref8 Shen (S0308210519000088_ref12) 2018; 269 S0308210519000088_ref9 S0308210519000088_ref2 S0308210519000088_ref3 Prange (S0308210519000088_ref10) 2013; 83 S0308210519000088_ref4 S0308210519000088_ref5 Shen (S0308210519000088_ref14) S0308210519000088_ref11 |
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| Snippet | For a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively... For a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively... For a family of elliptic operators with periodically oscillating coefficients, \(-{\rm div}(A(\cdot /\varepsilon )\nabla )\) with tiny ε > 0, we... |
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| SubjectTerms | Boundary layers Dirichlet problem Domains Eigenvalues Eigenvectors Homogenization |
| Title | First-order expansions for eigenvalues and eigenfunctions in periodic homogenization |
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