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In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Italian-Austrian mathematician Franz Rellich and the Russian mathematician Vladimir Iosifovich Kondrashov. Rellich proved the ''L''''2'' theorem and Kondrachov the ''L''''p'' theorem. ==Statement of the theorem== Let Ω ⊆ R''n'' be an open, bounded Lipschitz domain, and let 1 ≤ ''p'' < ''n''. Set : Then the Sobolev space ''W''1,''p''(Ω; R) is continuously embedded in the ''L''''p'' space ''L''''p''∗(Ω; R) and is compactly embedded in ''L''''q''(Ω; R) for every 1 ≤ ''q'' < ''p''∗. In symbols, : 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「Rellich–Kondrachov theorem」の詳細全文を読む スポンサード リンク
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