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In mathematics, Souček spaces are generalizations of Sobolev spaces, named after the Czech mathematician Jiří Souček. One of their main advantages is that they offer a way to deal with the fact that the Sobolev space ''W''1,1 is not a reflexive space; since ''W''1,1 is not reflexive, it is not always true that a bounded sequence has a weakly convergent subsequence, which is a desideratum in many applications. ==Definition== Let Ω be a bounded domain in ''n''-dimensional Euclidean space with smooth boundary. The Souček space ''W''1,''μ''(Ω; R''m'') is defined to be the space of all ordered pairs (''u'', ''v''), where * ''u'' lies in the Lebesgue space ''L''1(Ω; R''m''); * ''v'' (thought of as the gradient of ''u'') is a regular Borel measure on the closure of Ω; * there exists a sequence of functions ''u''''k'' in the Sobolev space ''W''1,1(Ω; R''m'') such that :: :and :: :weakly-∗ in the space of all R''m''×''n''-valued regular Borel measures on the closure of Ω. 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「Souček space」の詳細全文を読む スポンサード リンク
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