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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brezis–Gallouet inequality ： ウィキペディア英語版 Brezis–Gallouet inequality In mathematical analysis, the Brezis–Gallouet inequality,〔''Nonlinear Schrödinger evolution equation'', Nonlinear Analysis TMA 4, 677. (1980)〕 named after Haïm Brezis and Thierry Gallouet, is an inequality valid in 2 spatial dimensions. It shows that a function of two variables which is sufficiently smooth is (essentially) bounded, and provides an explicit bound, which depends only logarithmically on the second derivatives. It is useful in the study of partial differential equations. Let $u\backslash in\; H^2(\backslash Omega)$ where $\backslash Omega\backslash subset\backslash mathbb^2$. Then the Brézis–Gallouet inequality states that there exists a constant $C$ such that : $\backslash displaystyle\; \backslash |u\backslash |\_\backslash leq\; C\; \backslash |u\backslash |\_\backslash left(1+\backslash log\backslash frac,$ where $\backslash Delta$ is the Laplacian, and $\backslash lambda\_1$ is its first eigenvalue. ==See also== * Ladyzhenskaya inequality * Agmon's inequality 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brezis–Gallouet inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.