翻訳と辞書 Words near each other ・ Morrell Park, Baltimore ・ Morrell Park, Philadelphia ・ Morrell Point ・ Morrell Potrero ・ Morrell Reef ・ Morrell Siding, New Brunswick ・ Morrells Brewing Company ・ Morrells Corner, New Jersey ・ Morrells of Oxford Ltd v Oxford United Football Club ・ Morrelville, Illinois ・ Morrenia ・ Morrenia odorata ・ Morrens ・ Morretes ・ Morrey ・ Morrey–Campanato space ・ Morrice ・ Morrice James, Baron St Brides ・ Morrice, Michigan ・ Morrich More ・ Morricone Youth ・ Morrie ・ Morrie (musician) ・ Morrie Aderholt ・ Morrie Arnovich ・ Morrie Boyle ・ Morrie Brickman ・ Morrie Church ・ Morrie Critchley ・ Morrie Elis 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 Morrey–Campanato space ： ウィキペディア英語版 Morrey–Campanato space In mathematics, the Morrey–Campanato spaces (named after Charles B. Morrey, Jr. and Sergio Campanato) $L^(\backslash Omega)$ are Banach spaces which extend the notion of functions of bounded mean oscillation, describing situations where the oscillation of the function in a ball is proportional to some power of the radius other than the dimension. They are used in the theory of elliptic partial differential equations, since for certain values of $\backslash lambda$, elements of the space $L^(\backslash Omega)$ are Hölder continuous functions over the domain $\backslash Omega$. The seminorm of the Morrey spaces is given by :$\backslash left()\_^p\; =\; \backslash sup\_\; \backslash frac\; \backslash int\_\; |\; u(y)\; |^p\; dy.$ When $\backslash lambda\; =\; 0$, the Morrey space is the same as the usual $L^p$ space. When $\backslash lambda\; =\; n$, the spatial dimension, the Morrey space is equivalent to $L^\backslash infty$, due to the Lebesgue differentiation theorem. When $\backslash lambda\; >\; n$, the space contains only the 0 function. The seminorm of the Campanato space is given by :$\backslash left()\_^p\; =\; \backslash sup\_\; \backslash frac\; \backslash int\_\; |\; u(y)\; -\; u\_\; |^p\; dy$ where :$u\_\; =\; \backslash frac\; \backslash int\_\; u(y)\; dy.$ It is known that the Morrey spaces with are equivalent to the Campanato spaces with the same value of $\backslash lambda$ when $\backslash Omega$ is a sufficiently regular domain, that is to say, when there is a constant ''A'' such that $|\backslash Omega\; \backslash cap\; B\_r(x\_0)|\; >\; A\; r^n$ for every $x\_0\; \backslash in\; \backslash Omega$ and . When $n=\backslash lambda$, the Campanato space is the space of functions of bounded mean oscillation. When , the Campanato space is the space of Hölder continuous functions $C^\backslash alpha(\backslash Omega)$ with $\backslash alpha\; =\; \backslash frac$. For $\backslash lambda\; >\; n+p$, the space contains only constant functions. ==References== * * 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「Morrey–Campanato space」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.