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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analysis a class of Sobolevinequalities, relating norms including those of Sobolev spaces. These are used to prove the Sobolev embedding theorem, giving...
In mathematics, logarithmic Sobolevinequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient ∇ f {\displaystyle...
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...
The n-dimensional isoperimetric inequality is equivalent (for sufficiently smooth domains) to the Sobolevinequality on R n {\displaystyle \mathbb {R}...
Prof Sergei Lvovich Sobolev, FRSE (Russian: Серге́й Льво́вич Со́болев; 6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical...
In mathematics, the Riesz rearrangement inequality, sometimes called Riesz–Sobolevinequality, states that any three non-negative functions f : R n →...
non-integer Sobolev spaces, is also a special case of the Gagliardo-Nirenberg interpolation inequality. Denoting the L 2 {\displaystyle L^{2}} Sobolev spaces...
Chafaï, D. (2003), "Gaussian maximum of entropy and reversed log-Sobolevinequality", Séminaire de Probabilités XXXVI, Lecture Notes in Mathematics, vol...
E. Thirring, Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to SobolevInequalities, in Studies in...
The Sobolevinequality is equivalent to the isoperimetric inequality (in any dimension), with the same best constants. Wirtinger's inequality also generalizes...
{pn}{n-p}}>p} This is an important parameter in the Sobolevinequalities. A question arises whether u from the Sobolev space W 1 , p ( R n ) {\displaystyle W^{1...
Combining the coarea formula with the isoperimetric inequality gives a proof of the Sobolevinequality for W1,1 with best constant: ( ∫ R n | u | n n − 1...
any f ∈ L 2 ( Y ) {\displaystyle f\in L^{2}(Y)} . Hardy–Littlewood–Sobolevinequality Paul Richard Halmos and Viakalathur Shankar Sunder, Bounded integral...
fundamental inequalities for Sobolev spaces, now known as the Gagliardo–Nirenberg–Sobolevinequality and the Gagliardo–Nirenberg interpolation inequalities.[N59]...
+ 1 ) . {\displaystyle \|Rf\|_{(s)}\leq C'_{s}\|f\|_{(s+1)}.} The Sobolevinequality holds for f in Hs with s > 1/2: | f ( x ) | ≤ C s , k ‖ f ‖ ( s +...
spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic...
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