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Zeitschrift für Analysis und ihre Anwendungen


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Volume 30, Issue 3, 2011, pp. 355–375
DOI: 10.4171/ZAA/1439

Published online: 2011-07-03

Concentration-Compactness Principle for Generalized Trudinger Inequalities

Robert Černý[1], Petr Gurka[2] and Stanislav Hencl[3]

(1) Charles University, Prague, Czech Republic
(2) Czech University of Life Sciences, Prague, Czech Republic
(3) Charles University, Prague, Czech Republic

Let $\Omega\subset\mathbb R^n$, $n\geq 2$, be a bounded domain and let $\alpha < n-1$. We prove the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space $W^1_0L^n\log^{\alpha}L(\Omega)$ into the Orlicz space with the Young function $\exp\big(t^{\frac{n}{n-1-\alpha}}\big)-1$.

Keywords: Orlicz-Sobolev spaces, Concentration-Compactness

Černý Robert, Gurka Petr, Hencl Stanislav: Concentration-Compactness Principle for Generalized Trudinger Inequalities. Z. Anal. Anwend. 30 (2011), 355-375. doi: 10.4171/ZAA/1439