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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.

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rdfs:label	Disuguaglianza di Sobolev (it) ソボレフ不等式 (ja) Sobolev inequality (en) 索博列夫不等式 (zh)
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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dcterms:subject	Sobolev spaces Inequalities Compactness theorems
Wikipage page ID	4665038 (xsd:integer)
Wikipage revision ID	1117757836 (xsd:integer)
Link from a Wikipage to another Wikipage	American Journal of Mathematics Princeton University Press Rellich–Kondrachov theorem Riesz potential Riesz transform Compact space Compact support Mathematical analysis Mathematics Bounded mean oscillation Bounded set Cone condition Leonard Gross Lipschitz continuity Lp space Sobolev spaces Sobolev space Logarithmic Sobolev inequalities American Mathematical Society Collocation method Dirichlet form Riemannian manifold Inequalities Charles B. Morrey Jr. Compactness theorems Hölder continuous Hölder space Open set Masson (publisher) Compactly embedded Poincaré inequality Weak derivative Injectivity radius Sobolev conjugate Manifold with boundary Sectional curvature Springer-Verlag Fractional integration Complete manifold Completely continuous Sergei Lvovich Sobolev N sphere Springer Science & Business Media
Link from a Wikipage to an external page	http://bookstore.ams.org/gsm-105 http://www.maa.org/press/maa-reviews/a-first-course-in-sobolev-spaces https://archive.org/details/singularintegral0000stei
sameAs	Sobolev inequality Sobolev inequality Sobolev inequality Sobolev inequality Sobolev inequality Sobolev inequality Sobolev inequality
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