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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 Interpolation inequality ： ウィキペディア英語版 Interpolation inequality In the field of mathematical analysis, an interpolation inequality is an inequality of the form :$$ \| u_ \|_ \leq C \| u_ \|_^ \|_^ \|_^^} | u(x) |^ \, \mathrm x \leq 2 \int_} | u(x) |^ \, \mathrm x \int_} | \nabla u(x) |^ \, \mathrm x, i.e. :$$ \| u \|_ \, \| u \|_ \, \| \nabla u \|_. (Since Ladyzhenskaya's inequality considers compactly supported functions ''u'', Friedrichs' inequality implies that the ''L''2 norm of ∇''u'' is equivalent to the ''H''1 Sobolev norm of ''u'', and so Ladyzhenskaya's inequality really does only treat a single function ''u'', not distinct functions ''u''0 = ''u''1 = ''u'' and ''u''2 = ∇''u''.) Another simple example of an interpolation inequality — one in which the ''u''''k'' and the norms ‖·‖''k'' are different — is Young's inequality for the convolution of two functions ''f'', ''g'': ℝ''d'' → ℝ: :$\backslash |f\; \backslash star\; g\backslash |\_\}\; \backslash |g\backslash |\_+\backslash frac=1+\backslash frac.$ ==Examples of interpolation inequalities== * Agmon's inequality * Gagliardo–Nirenberg interpolation inequality * Ladyzhenskaya's inequality * Landau–Kolmogorov inequality * Marcinkiewicz interpolation theorem * Nash's inequality * Riesz–Thorin theorem * Young's inequality for convolutions 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「Interpolation inequality」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.