Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 90, pp. 1-15.

Title: Compactness results for quasilinear problems with variable
       exponent on the whole space
       
Authors: Olfa Allegue (Inst. Prep. d'ingenieurs de Tunis, Tunisia)
         Asma Karoui Souayah (Inst. Prep. d'ingenieurs de Tunis, Tunisia)

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 06, 2011.
Math Subject Classifications: 35J655, 35J60, 35J70, 58E05.
Key Words: p(x)-Laplace operator;  critical Sobolev exponent;
           compactness; Palais-Smale condition.