翻訳と辞書 Words near each other ・ Fundamental frequency ・ Fundamental Fysiks Group ・ Fundamental group ・ Fundamental group scheme ・ Fundamental human needs ・ Fundamental increment lemma ・ Fundamental interaction ・ Fundamental interpersonal relations orientation ・ Fundamental justice ・ Fundamental law ・ Fundamental Law of Education ・ Fundamental Law of Vatican City State ・ Fundamental Laws of England ・ Fundamental Laws of the Realm ・ Fundamental lemma (Langlands program) ・ Fundamental lemma of calculus of variations ・ Fundamental lemma of sieve theory ・ Fundamental Love ・ Fundamental matrix ・ Fundamental matrix (computer vision) ・ Fundamental matrix (linear differential equation) ・ Fundamental Methodist Conference, Inc. ・ Fundamental modeling concepts ・ Fundamental normality test ・ Fundamental ontology ・ Fundamental Orders of Connecticut ・ Fundamental pair of periods ・ Fundamental parallelogram ・ Fundamental pattern ・ Fundamental Physics Prize 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 Fundamental lemma of calculus of variations ： ウィキペディア英語版 Fundamental lemma of calculus of variations In mathematics, specifically in the calculus of variations, a variation of a function can be concentrated on an arbitrarily small interval, but not a single point. Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function . The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation (differential equation), free of the integration with arbitrary function. The proof usually exploits the possibility to choose concentrated on an interval on which keeps sign (positive or negative). Several versions of the lemma are in use. Basic versions are easy to formulate and prove. More powerful versions are used when needed. ==Basic version== :If a continuous function ''f'' on an open interval (''a'',''b'') satisfies the equality ::$\backslash int\_a^b\; f(x)\; \backslash ,\; h(x)\; \backslash ,\; \backslash mathrmx\; =\; 0$ :for all compactly supported smooth functions ''h'' on (''a'',''b''), then ''f'' is identically zero. Here "smooth" may be interpreted as "infinitely differentiable",〔 but often is interpreted as "twice continuously differentiable" or "continuously differentiable" or even just "continuous",〔 since these weaker statements may be strong enough for a given task. "Compactly supported" means "vanishes outside () for some ''c'',''d'' such that ''a''<''c''<''d''<''b''";〔 but often a weaker statement suffices, assuming only that ''h'' (or ''h'' and a number of its derivatives) vanishes at the endpoints ''a'', ''b'';〔 in this case the closed interval () is used. 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「Fundamental lemma of calculus of variations」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.