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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 Hilbert's nineteenth problem ： ウィキペディア英語版 Hilbert's nineteenth problem Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a celebrated list compiled in 1900 by David Hilbert.〔See or, equivalently, one of its translations.〕 It asks whether the solutions of regular problems in the calculus of variations are always analytic.〔"''Sind die Lösungen regulärer Variationsprobleme stets notwending analytisch?''" (English translation by Mary Frances Winston Newson:-"''Are the solutions of regular problems in the calculus of variations always necessarily analytic?''"), formulating the problem with the same words of .〕 Informally, and perhaps less directly, since Hilbert's concept of a "''regular variational problem''" identifies precisely a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients.〔See , or the corresponding section on the nineteenth problem in any of its translation or reprint, or the subsection "The origins of the problem" in the historical section of this entry.〕 Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution function inherits the relatively simple and well understood structure from the solved equation. ==History== 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「Hilbert's nineteenth problem」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.