翻訳と辞書 Words near each other ・ AGM-87 Focus ・ AGM-88 HARM ・ AGMA ・ Agma Lahlou-Tazi ・ Agmark ・ Agmatidine ・ Agmatinase ・ Agmatine ・ Agmatine deiminase ・ Agmatine kinase ・ Agmatine N4-coumaroyltransferase ・ AGMC ・ AgMES ・ AGML ・ Agmon ・ Agmon's inequality ・ Agmondesham Vesey ・ Agmostigma ・ Agmé ・ AGN ・ AGN-2979 ・ Agna ・ Agnaadi ・ Agnac ・ Agnack Grand ・ Agnack Petit ・ Agnadello ・ Agnafit ・ Agnaldo (footballer, born 1994) ・ Agnaldo Cordeiro Pereira Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Agmon's inequality ： ウィキペディア英語版 Agmon's inequality In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon,〔Lemma 13.2, in: Agmon, Shmuel, ''Lectures on Elliptic Boundary Value Problems'', AMS Chelsea Publishing, Providence, RI, 2010. ISBN 978-0-8218-4910-1.〕 consist of two closely related interpolation inequalities between the Lebesgue space $L^\backslash infty$ and the Sobolev spaces $H^s$. It is useful in the study of partial differential equations. Let $u\backslash in\; H^2(\backslash Omega)\backslash cap\; H^1\_0(\backslash Omega)$ where $\backslash Omega\backslash subset\backslash mathbb^3$. Then Agmon's inequalities in 3D state that there exists a constant $C$ such that : $\backslash displaystyle\; \backslash |u\backslash |\_\backslash leq\; C\; \backslash |u\backslash |\_^\; \backslash |u\backslash |\_^,$ and : $\backslash displaystyle\; \backslash |u\backslash |\_\backslash leq\; C\; \backslash |u\backslash |\_^\; \backslash |u\backslash |\_^.$ In 2D, the first inequality still holds, but not the second: let $u\backslash in\; H^2(\backslash Omega)\backslash cap\; H^1\_0(\backslash Omega)$ where $\backslash Omega\backslash subset\backslash mathbb^2$. Then Agmon's inequality in 2D states that there exists a constant $C$ such that : $\backslash displaystyle\; \backslash |u\backslash |\_\backslash leq\; C\; \backslash |u\backslash |\_^\; \backslash |u\backslash |\_^.$ For the $n$-dimensional case, choose $s\_1$ and $s\_2$ such that . Then, if and $\backslash tfrac\; =\; \backslash theta\; s\_1\; +\; (1-\backslash theta)s\_2$, the following inequality holds for any $u\backslash in\; H^(\backslash Omega)$ : $\backslash displaystyle\; \backslash |u\backslash |\_\backslash leq\; C\; \backslash |u\backslash |\_^\; \backslash |u\backslash |\_^$ ==See also== * Ladyzhenskaya inequality * Brezis–Gallouet 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「Agmon's 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.