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Taylor’s theorem for functionals on BMO with application to BMO local minimizers
https://oist.repo.nii.ac.jp/records/1983
https://oist.repo.nii.ac.jp/records/1983b8d76b11-f1da-4aa4-927a-2b56531b659a
名前 / ファイル | ライセンス | アクション |
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Spectors-BMO-R1 (111.3 kB)
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International(https://creativecommons.org/licenses/by-nc-nd/4.0/)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2021-03-18 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Taylor’s theorem for functionals on BMO with application to BMO local minimizers | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
著者(英) |
Spector, Daniel E.
× Spector, Daniel E.× Spector, Scott J. |
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書誌情報 |
en : Quarterly of Applied Mathematics 発行日 2020-10-06 |
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抄録 | ||||||
内容記述タイプ | Other | |||||
内容記述 | In this note two results are established for energy functionals that are given by the integral of W(x,∇u(x)) over Ω⊂Rn with ∇u∈BMO(Ω;RN×n), the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand W has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in W1,BMO(Ω;RN), the subspace of the Sobolev space W1,1(Ω;RN) for which the weak derivative ∇u∈BMO(Ω;RN×n). | |||||
出版者 | ||||||
出版者 | American Mathematical Society | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0033-569X | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 1552-4485 | |||||
DOI | ||||||
関連タイプ | isVersionOf | |||||
識別子タイプ | DOI | |||||
関連識別子 | info:doi/10.1090/qam/1586 | |||||
権利 | ||||||
権利情報 | © 2020 Brown University | |||||
権利 | ||||||
権利情報 | First published in Quart. Appl. Math. (October 2020), published by the American Mathematical Society. | |||||
関連サイト | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://www.ams.org/journals/qam/0000-000-00/S0033-569X-2020-01586-X/ | |||||
著者版フラグ | ||||||
出版タイプ | AM | |||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa |