Abstract
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 [Cerny 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 (W0Ln)-L-1 log(alpha) L(Omega) into the Orlicz space corresponding to a Young function that behaves like exp t(n/(n-1-alpha)) for large t. We also give the result for the case of the embedding into double and other multiple exponential spaces.