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Sobolev space

In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing…

Motivation, Overview & Sobolev spaces with integer k

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Overview

Motivation

Sobolev spaces with integer k

Traces

Sobolev spaces with non-integer k

Extension operators

Sobolev embeddings

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Sobolev space

Nodes82
Edges81
Triples158
Avg. degree1.98
Density0.02439
Components1

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Sobolev space

Top relations

related to References · 99
Sobolev space → Academic Press, Adams, Alessandra, Amer, American Mathematical Society, American Mathematical Society Translations, An Introduction, Analysis, Analytic, Applied Mathematics, Aubin, Bad Domains, Basel, Bergh, Berlin, Birkhäuser Verlag, Boston, Date, Differentiability Properties, Differentiable Functions
related to Sobolev embeddings · 11
Sobolev space → Cn, For, Here, Hölder, It, Riemannian, Roughly, Sobolev, The Sobolev, This, Write
related to Traces · 11
Sobolev space → Assume, However, If, It, Lipschitz, Omega, Sobolev, The, Then, Trace, Tu
related to Sobolev–Slobodeckij spaces · 9
Sobolev space → Another, For, Hölder, Let, Lp-setting, Omega, Slobodeckij, Sobolev, Using
related to Motivation · 8
Sobolev space → Differentiability, Differentiable, In, Omega, The, The Sobolev, There, Throughout
related to One-dimensional case · 7
Sobolev space → As, Cantor's, In, Lebesgue, Lp, Sobolev, With
related to External links · 5
Sobolev space → Eleonora Di Nezza, Enrico Valdinoci, Giampiero Palatucci, Hitchhiker's, Sobolev
related to Multidimensional case · 4
Sobolev space → Let, Omega, The, The Sobolev
is a · 2
Sobolev space → space of functions possessing sufficiently many derivatives for some application domain, vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order

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Important terminology

displaystyle sobolev omega space functions spaces continuous mathbb norm weak function partial derivatives infty defined isbn sense derivative boundary differential

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Sobolev spaceis avector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order0.90text
Sobolev spaceis aspace of functions possessing sufficiently many derivatives for some application domain0.90text
Cantor's functioninstance ofthis excludes irrelevant examples0.80text
R ninstance ofInformally these embeddings say that to convert an Lp estimate to a boundedness estimate costs 1/p derivatives per dimension.There are similar variations of the embedding theore…0.80text
Sobolev spacerelated to External linksEleonora Di Nezza0.60section
Sobolev spacerelated to External linksGiampiero Palatucci0.60section
Sobolev spacerelated to External linksEnrico Valdinoci0.60section
Sobolev spacerelated to External linksHitchhiker's0.60section
Sobolev spacerelated to External linksSobolev0.60section
Sobolev spacerelated to MotivationThroughout0.60section
Sobolev spacerelated to MotivationOmega0.60section
Sobolev spacerelated to MotivationThere0.60section

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