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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 Lions–Lax–Milgram theorem ： ウィキペディア英語版 Lions–Lax–Milgram theorem In mathematics, the Lions–Lax–Milgram theorem (or simply Lions’ theorem) is a result in functional analysis with applications in the study of partial differential equations. It is a generalization of the famous Lax–Milgram theorem, which gives conditions under which a bilinear function can be "inverted" to show the existence and uniqueness of a weak solution to a given boundary value problem. The result is named after the mathematicians Jacques-Louis Lions, Peter Lax and Arthur Milgram. ==Statement of the theorem== Let ''H'' be a Hilbert space and ''V'' a normed space. Let ''B'' : ''H'' × ''V'' → R be a continuous, bilinear function. Then the following are equivalent: * (coercivity) for some constant ''c'' > 0, ::$\backslash inf\_\; \backslash sup\_\; |\; B(h,\; v)\; |\; \backslash geq\; c;$ * (existence of a "weak inverse") for each continuous linear functional ''f'' ∈ ''V''∗, there is an element ''h'' ∈ ''H'' such that ::$B(h,\; v)\; =\; \backslash langle\; f,\; v\; \backslash rangle\; \backslash mbox\; v\; \backslash in\; V.$ 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「Lions–Lax–Milgram theorem」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.