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 of the exponent concerning the Concentration-Compactness Principle for the embedding of the Orlicz-Sobolev space W 01 L n logα L(Ω) into the Orlicz space corresponding to a Young function that behaves like exp t n/(n−1−α) for large t. We also give the result for the case of the embedding into double and other multiple exponential spaces.
@article{bwmeta1.element.doi-10_2478_s11533-011-0102-3,
author = {Robert \v Cern\'y},
title = {Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {590-602},
zbl = {1272.46019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0102-3}
}
Robert Černý. Note on the concentration-compactness principle for generalized Moser-Trudinger inequalities. Open Mathematics, Tome 10 (2012) pp. 590-602. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0102-3/
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