Extrapolation of Sobolev imbeddings.

M. Krbec

Displaying similar documents to “Extrapolation of Sobolev imbeddings.”

An embedding theorem for Sobolev type functions with gradients in a Lorentz space

Alireza Ranjbar-Motlagh (2009)

Studia Mathematica

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The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

On equivalence of super log Sobolev and Nash type inequalities

Marco Biroli, Patrick Maheux (2014)

Colloquium Mathematicae

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We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon's counterexample as the borderline case of this equivalence and related open problems.

On factorization of Fefferman's inequality

Krbec, Miroslav, Schott, Thomas

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Weighted Sobolev spaces and capacity.

Kilpeläinen, Tero (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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The sharp Sobolev inequality in quantitative form

Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)

Journal of the European Mathematical Society

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Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems

Andrea Cianchi (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

Addendum to the paper "On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem"

A. Pełczyński, K. Senator (1986)

Studia Mathematica

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Approximation and entropy numbers of embeddings in weighted Orlicz spaces

David Eric Edmunds, Jiong Sun (1991)

Mathematica Bohemica

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Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.

Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $n \geq 2$ and $Ω \subset ℝ^{n}$ be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space $W_{0} L^{Φ} (Ω)$ , where the Young function $Φ$ behaves like $t^{n} {log}^{α} (t)$ , $α < n - 1$ , for $t$ large, into the Zygmund space $Z_{0}^{\frac{n - 1 - α}{n}} (Ω)$ . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space $W_{0}^{m} L^{\frac{n}{m}, q} {log}^{α} L (Ω)$ , $m < n$ , $q \in (1, \infty]$ , $α < \frac{1}{q^{'}}$ , embedded into the Zygmund space $Z_{0}^{\frac{1}{q^{'}} - α} (Ω)$ .