Geodesic
Compactness results for quasilinear problems with variable exponent on the whole space
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a41/}
}
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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/