Geodesic
Compactness results for quasilinear problems with variable exponent on the whole space
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 35J655, 35J60, 35J70, 58E05
Keywords: $p(x)$-Laplace operator, critical Sobolev exponent, compactness, palais-Smale condition 
@article{EJDE_2011__2011__a41,
     author = {Allegue,  Olfa and Souayah,  Asma Karoui},
     title = {Compactness results for quasilinear problems with variable exponent on the whole space},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1229.35333},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a41/}
}
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%A Souayah,  Asma Karoui
%T Compactness results for quasilinear problems with variable exponent on the whole space
%J Electronic journal of differential equations
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%V 2011
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%F EJDE_2011__2011__a41
Allegue,  Olfa; Souayah,  Asma Karoui. Compactness results for quasilinear problems with variable exponent on the whole space. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a41/