| dbo:abstract |
In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others. They are named after Sergei Lvovich Sobolev. (en) 数学の解析学の分野には、ソボレフ空間のノルムを含むノルムに関して、ソボレフ不等式（ソボレフふとうしき、英: Sobolev inequality）の類が存在する。それらは、ある種のソボレフ空間の間の包含関係を与えるソボレフ埋蔵定理（Sobolev embedding theorem）や、わずかに強い条件の下でいくつかのソボレフ空間は別のものにコンパクトに埋め込まれることを示すレリッヒ＝コンドラショフの定理を証明するために用いられる。セルゲイ・ソボレフの名にちなむ。 (ja) In matematica, in particolare nel campo dell'analisi matematica, una disuguaglianza di Sobolev rientra in una classe di disuguaglianze, il cui nome si deve a Sobolev, riguardanti le norme definite negli spazi di Sobolev. Esse sono utilizzate per dimostrare il teorema di immersione di Sobolev (sulle inclusioni tra alcuni spazi di Sobolev) ed il teorema di Rellich-Kondrakov (secondo cui, sotto condizioni leggermente più forti, alcuni spazi di Sobolev sono contenuti con compattezza in altri). (it) 在数学分析中有一类关于索博列夫空间中的范数的索博列夫不等式（英語：Sobolev inequality; 俄语：Соболев неравенство）。 这些不等式可以用于证明索博列夫嵌入定理，给出某些索博列夫空间的包含关系。而指出在稍强的条件下，一些索博列夫空间可以被到另一个空间。这类不等式得名于苏联数学家谢尔盖·利沃维奇·索博列夫。 (zh) |
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http://bookstore.ams.org/gsm-105 http://www.maa.org/press/maa-reviews/a-first-course-in-sobolev-spaces https://archive.org/details/singularintegral0000stei |
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John Forbes Nash, Jr. (en) |
| dbp:first |
John (en) S.M. (en) |
| dbp:id |
i/i050230 (en) |
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Nash (en) Nikol'skii (en) |
| dbp:title |
Imbedding theorems (en) |
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1958 (xsd:integer) |
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| rdfs:comment |
In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others. They are named after Sergei Lvovich Sobolev. (en) 数学の解析学の分野には、ソボレフ空間のノルムを含むノルムに関して、ソボレフ不等式（ソボレフふとうしき、英: Sobolev inequality）の類が存在する。それらは、ある種のソボレフ空間の間の包含関係を与えるソボレフ埋蔵定理（Sobolev embedding theorem）や、わずかに強い条件の下でいくつかのソボレフ空間は別のものにコンパクトに埋め込まれることを示すレリッヒ＝コンドラショフの定理を証明するために用いられる。セルゲイ・ソボレフの名にちなむ。 (ja) In matematica, in particolare nel campo dell'analisi matematica, una disuguaglianza di Sobolev rientra in una classe di disuguaglianze, il cui nome si deve a Sobolev, riguardanti le norme definite negli spazi di Sobolev. Esse sono utilizzate per dimostrare il teorema di immersione di Sobolev (sulle inclusioni tra alcuni spazi di Sobolev) ed il teorema di Rellich-Kondrakov (secondo cui, sotto condizioni leggermente più forti, alcuni spazi di Sobolev sono contenuti con compattezza in altri). (it) 在数学分析中有一类关于索博列夫空间中的范数的索博列夫不等式（英語：Sobolev inequality; 俄语：Соболев неравенство）。 这些不等式可以用于证明索博列夫嵌入定理，给出某些索博列夫空间的包含关系。而指出在稍强的条件下，一些索博列夫空间可以被到另一个空间。这类不等式得名于苏联数学家谢尔盖·利沃维奇·索博列夫。 (zh) |
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Disuguaglianza di Sobolev (it) ソボレフ不等式 (ja) Sobolev inequality (en) 索博列夫不等式 (zh) |
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