Displaying similar documents to “Sharp generalized Trudinger inequalities via truncation for embedding into multiple exponential spaces”

On generalized Moser-Trudinger inequalities without boundary condition

Robert Černý (2012)

Czechoslovak Mathematical Journal

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We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.

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...

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 ∫ B u 2 ⁢ x ⁢ V ⁢ x ⁢ d ⁢ x 1 2 ≤ c ⁢ ∫ B ∇ ⁡ u ⁢ x 2 ⁢ d ⁢ x 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 ≤ V ⁢ u nelle dimensioni 2 e 3. ...

Double exponential integrability, Bessel potentials and embedding theorems

David Edmunds, Petr Gurka, Bohumír Opic (1995)

Studia Mathematica

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This paper is a continuation of [5] and provides necessary and sufficient conditions for double exponential integrability of the Bessel potential of functions from suitable (generalized) Lorentz-Zygmund spaces. These results are used to establish embedding theorems for Bessel potential spaces which extend Trudinger's result.