Decomposition and Moser's lemma.

David E. Edmunds; Miroslav Krbec

Displaying similar documents to “Decomposition and Moser's lemma.”

A summability condition on the gradient ensuring BMO.

Alberto Fiorenza (1998)

Revista Matemática Complutense

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Superposition of imbeddings and Fefferman's inequality

Miroslav Krbec, Thomas Schott (1999)

Bollettino dell'Unione Matematica Italiana

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In questo lavoro si studiano condizioni sufficienti sulla funzione peso $V$ , espresse in termini di integrabilità, per la validità della disuguaglianza ${(\int_{B} u^{2} (x) V (x) d x)}^{\frac{1}{2}} \leq c {(\int_{B} {(\nabla u (x))}^{2} d x)}^{\frac{1}{2}},$ dove $B$ denota una sfera in $R^{N}$ . Usando una tecnica di decomposizione di immersioni si dimostrano condizioni sufficienti in termini di appartenenza a spazi di Lebesgue, Lorentz-Orlicz e/o di tipo debole. Come applicazioni vengono fornite condizioni sufficienti per la proprietà forte di prolungamento unico per $|Δ u| \leq V |u|$ nelle dimensioni 2 e 3. ...

Sharp generalized Trudinger inequalities via truncation for embedding into multiple exponential spaces

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that the generalized Trudinger inequality for Orlicz-Sobolev spaces embedded into multiple exponential spaces implies a version of an inequality due to Brézis and Wainger.

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 $Z_{0}^{\frac{1}{q^{'}} - α} (Ω)$ .

Mappings with dilatation in Orlicz spaces.

Jana Björn (2002)

Collectanea Mathematica

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Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities

Robert Černý (2012)

Open Mathematics

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Let Ω ⊂ ℝn, n ≥ 2, be a bounded domain and let α < n − 1. Motivated by Theorem I.6 and Remark I.18 of [Lions P.-L., The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana, 1985, 1(1), 145–201] and by the results of [Černý R., Cianchi A., Hencl S., Concentration-Compactness Principle for Moser-Trudinger inequalities: new results and proofs, Ann. Mat. Pura Appl. (in press), DOI: 10.1007/s10231-011-0220-3], we give a sharp estimate...