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 |
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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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