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Sobolev inequality

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…

Sobolev embedding theorem, Gagliardo–Nirenberg–Sobolev inequality & Hardy–Littlewood–Sobolev lemma

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Sobolev embedding theorem

Weak derivativesLpSobolev conjugateNečas 2012Hölder spaces
16 related topics

Gagliardo–Nirenberg–Sobolev inequality

Compact supportGagliardoNirenberg
3 related topics

Hardy–Littlewood–Sobolev lemma

Fractional integrationRiesz potentialRiesz transforms
3 related topics

Nash inequality

JohnNashFourier transformN-ball
3 related topics

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Overview

Sobolev embedding theorem

Gagliardo–Nirenberg–Sobolev inequality

Hardy–Littlewood–Sobolev lemma

Morrey's inequality

Case p=n, k=1

Nash inequality

Logarithmic Sobolev inequality

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Sobolev inequality

Nodes47
Edges46
Triples8
Avg. degree1.96
Density0.042553
Components1

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Sobolev inequality

Top relations

related to Gagliardo–Nirenberg–Sobolev inequality · 8
Sobolev inequality → Assume, Gagliardo, Nirenberg, Rn, Sobolev, The, The Gagliardo, Then

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Important terminology

sobolev displaystyle embedding inequality theorem rn bounded one function spaces mathematics constant case space continuous inequalities mathbf boundary depending estimate

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SubjectPredicateObjectConfidenceSrc
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityAssume0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityRn0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityThen0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityThe0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalitySobolev0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityGagliardo0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityNirenberg0.60section
Sobolev inequalityrelated to Gagliardo–Nirenberg–Sobolev inequalityThe Gagliardo0.60section

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