翻訳と辞書 Words near each other ・ P. bakeri ・ P. Balachandran ・ P. Balasubramanian ・ P. Balasundarampillai ・ P. Ballantine and Sons Brewing Company ・ P. Balsara ・ P. Bharathiraja ・ P. Bhaskaran ・ P. bicolor ・ P. bidentata ・ P. Blaud ・ P. Booker Reed ・ P-group generation algorithm ・ P-hydroxybenzoate hydroxylase ・ P-Hydroxynorephedrine ・ P-Laplacian ・ P-Magazine ・ P-matrix ・ P-Menthane-3,8-diol ・ P-Model ・ P-Model (album) ・ P-Modeling Framework ・ P-Money ・ P-nuclei ・ P-O-X ・ P-P ・ P-P Hartnett ・ P-Patch ・ P-Phenylenediamine ・ P-Pop-High School 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 P-Laplacian ： ウィキペディア英語版 P-Laplacian In mathematics, the ''p''-Laplacian, or the ''p''-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a generalization of the Laplace operator, where $p$ is allowed to range over . It is written as :$\backslash nabla\; \backslash cdot\; (|\backslash nabla\; u|^\; \backslash nabla\; u).$ Where the $|\backslash nabla\; \backslash cdot\; |^$ operator is defined as $\backslash quad\; |\backslash nabla\; u|^\; =\; \backslash left(\backslash textstyle\; \backslash left(\backslash frac\backslash right)^2$ + \cdots + \left(\frac\right)^2 \right )^\frac In the special case when $p=2$, it is the regular Laplacian. 〔Evans, pp 356.〕 == Energy formulation == The solution of the ''p''-Laplace equation with Dirichlet boundary conditions :$\backslash nabla\; \backslash cdot\; (|\backslash nabla\; u|^\; \backslash nabla\; u)\; =\; 0$ in a domain $\backslash Omega$ is the minimizer of the energy functional :$J(u)\; =\; \backslash int\; |\backslash nabla\; u|^p\; \backslash ,dx$ among all functions in the Sobolev space $W^(\backslash Omega)$ satisfying the boundary conditions in the trace sense.〔 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「P-Laplacian」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.