Electron. J. Diff. Equ., Vol. 2011 (2011), No. 90, pp. 1-15.

Compactness results for quasilinear problems with variable exponent on the whole space

Olfa Allegue, Asma Karoui Souayah

Abstract:
In this work we give a compactness result which allows us to prove the point-wise convergence of the gradients of a sequence of solutions to a quasilinear inequality and for an arbitrary open set. This result suggests solutions to many problems, notably nonlinear elliptic problems with critical exponent.

Submitted May 2, 2011. Published July 6, 2011.
Math Subject Classifications: 35J655, 35J60, 35J70, 58E05.
Key Words: p(x)-Laplace operator; critical Sobolev exponent; compactness; Palais-Smale condition.

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Olfa Allegue
Institut Préparatoire aux Etudes d'ingénieurs de Tunis
2 Rue Jawaher Lel Nehru, 1008
Montfleury-Tunis, Tunisia
email: allegue_olfa@yahoo.fr
Asma Karoui Souayah
Institut Préparatoire aux Etudes d'ingénieurs de Tunis
2 Rue Jawaher Lel Nehru, 1008
Montfleury-Tunis, Tunisia
email: asma.souayah@yahoo.fr

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