翻訳と辞書 Words near each other ・ Weyl algebra ・ Weyl character formula ・ Weyl curvature hypothesis ・ Weyl distance function ・ Weyl equation ・ Weyl group ・ Weyl integral ・ Weyl law ・ Weyl metrics ・ Weyl module ・ Weyl scalar ・ Weyl semimetal ・ Weyl tensor ・ Weyl transformation ・ Weyl's inequality ・ Weyl's lemma (Laplace equation) ・ Weyl's postulate ・ Weyl's theorem ・ Weyl's theorem on complete reducibility ・ Weyl's tile argument ・ Weylan Harding ・ Weyland ・ Weyland ringtail possum ・ Weylin Hotel ・ Weyl–Brauer matrices ・ Weyl–Schouten theorem ・ Weyl–von Neumann theorem ・ Weyl−Lewis−Papapetrou coordinates ・ Weyman ・ Weyman Airpark 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 Weyl's lemma (Laplace equation) ： ウィキペディア英語版 Weyl's lemma (Laplace equation) In mathematics, Weyl's lemma, named after Hermann Weyl, states that every weak solution of Laplace's equation is a smooth solution. This contrasts with the wave equation, for example, which has weak solutions that are not smooth solutions. Weyl's lemma is a special case of elliptic or hypoelliptic regularity. ==Statement of the lemma== Let $\backslash Omega$ be an open subset of $n$-dimensional Euclidean space $\backslash mathbb^$, and let $\backslash Delta$ denote the usual Laplace operator. Weyl's lemma〔Hermann Weyl, The method of orthogonal projections in potential theory, ''Duke Math. J.'', 7, 411-444 (1940). See Lemma 2, p. 415〕 states that if a locally integrable function $u\; \backslash in\; L\_(\backslash Omega)$ is a weak solution of Laplace's equation, in the sense that :$\backslash int\_\; u(x)\; \backslash Delta\; \backslash phi\; (x)\; \backslash ,\; dx\; =\; 0$ for every smooth test function $\backslash phi\; \backslash in\; C\_c^\backslash infty(\backslash Omega)$ with compact support, then (up to redefinition on a set of measure zero) $u\; \backslash in\; C^(\backslash Omega)$ is smooth and satisfies $\backslash Delta\; u\; =\; 0$ pointwise in $\backslash Omega$. This result implies the interior regularity of harmonic functions in $\backslash Omega$, but it does not say anything about their regularity on the boundary $\backslash partial\backslash Omega$. 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「Weyl's lemma (Laplace equation)」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.