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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 Lipschitz domain ： ウィキペディア英語版 Lipschitz domain In mathematics, a Lipschitz domain (or domain with Lipschitz boundary) is a domain in Euclidean space whose boundary is "sufficiently regular" in the sense that it can be thought of as locally being the graph of a Lipschitz continuous function. The term is named after the German mathematician Rudolf Lipschitz. ==Definition== Let ''n'' ∈ N, and let Ω be an open subset of R''n''. Let ∂Ω denote the boundary of Ω. Then Ω is said to have Lipschitz boundary, and is called a Lipschitz domain, if, for every point ''p'' ∈ ∂Ω, there exists a radius ''r'' > 0 and a map ''h''''p'' : ''B''''r''(''p'') → ''Q'' such that * ''h''''p'' is a bijection; * ''h''''p'' and ''h''''p''−1 are both Lipschitz continuous functions; * ''h''''p''(∂Ω ∩ ''B''''r''(''p'')) = ''Q''0; * ''h''''p''(Ω ∩ ''B''''r''(''p'')) = ''Q''+; where : denotes the ''n''-dimensional open ball of radius ''r'' about ''p'', ''Q'' denotes the unit ball ''B''1(0), and :$Q\_\; :=\; \backslash )\; \backslash in\; Q\; |\; x\_\; =\; 0\; \backslash \};$ :$Q\_\; :=\; \backslash )\; \backslash in\; Q\; |\; x\_\; >\; 0\; \backslash \}.$ 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「Lipschitz domain」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.