C. O. Alves and Y. H. Ding, Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity, Journal of Mathematical Analysis and Applications, vol.279, issue.2, pp.508-521, 2003.
DOI : 10.1016/S0022-247X(03)00026-X

C. O. Alves and A. Hamidi, Existence of solution for a anisotropic equation with critical exponent, Differential Integral Equations, vol.21, issue.1, pp.25-40, 2008.

S. Antontsev, J. I. Díaz, and S. Shmarev, Energy methods for free boundary problems: Applications to nonlinear PDEs and fluid mechanics, Progress in Nonlinear Differential Equations and their Applications, 2002.
DOI : 10.1007/978-1-4612-0091-8

S. Antontsev and S. Shmarev, Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions, Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions, Handbook of Differential Equations: Stationary Partial Differential Equations, pp.728-761, 2006.
DOI : 10.1016/j.na.2005.09.035

G. Arioli and F. Gazzola, Some results on p-Laplace equations with a critical growth term, Differential Integral Equations, vol.11, issue.2, pp.311-326, 1998.

J. Bear, Dynamics of Fluids in Porous Media, Soil Science, vol.120, issue.2, 1972.
DOI : 10.1097/00010694-197508000-00022

R. D. Benguria, J. Dolbeault, and M. J. Esteban, Classification of the Solutions of Semilinear Elliptic Problems in a Ball, Journal of Differential Equations, vol.167, issue.2, pp.438-466, 2000.
DOI : 10.1006/jdeq.2000.3792

M. Bendahmane and K. H. Karlsen, Renormalized solutions of an anisotropic reaction-diffusion-advection system with L 1 data [10] , Nonlinear anisotropic elliptic and parabolic equations in R N with advection and lower order terms and locally integrable data, Potential Anal, Commun. Pure Appl. Anal, vol.5, issue.4 3, pp.733-762, 2005.

M. Bendahmane, M. Langlais, and M. Saad, On some anisotropic reaction-diffusion systems with L 1 -data modeling the propagation of an epidemic disease, Nonlinear Anal, pp.617-636, 2003.

H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer, pp.486-490, 1983.

A. Cianchi, Symmetrization in Anisotropic Elliptic Problems, Communications in Partial Differential Equations, vol.5, issue.5, pp.693-717, 2007.
DOI : 10.1007/BF02411942

F. Demengel and E. Hebey, On some nonlinear equations involving the p-Laplacian with critical Sobolev growth [16] , On some nonlinear equations involving the p-Laplacian with critical Sobolev growth and perturbation terms, Adv. Differential Equations Appl. Anal, vol.3, issue.72 12, pp.533-574, 1998.

A. and D. Castro, Existence and regularity results for anisotropic elliptic problems, Adv. Nonlin. Stud, vol.9, pp.367-393, 2009.

A. , D. Castro, and E. Montefusco, Nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations, Nonlinear Anal, pp.4093-4105, 2009.

A. Hamidi and J. Rakotoson, On a perturbed anisotropic equation with a critical exponent, Ricerche di Matematica, vol.55, issue.1, pp.55-69, 2006.
DOI : 10.1007/s11587-006-0004-z

URL : https://hal.archives-ouvertes.fr/hal-00347981

A. Hamidi and J. Vétois, Sharp Sobolev Asymptotics for Critical Anisotropic Equations, Archive for Rational Mechanics and Analysis, vol.16, issue.1, pp.1-36, 2009.
DOI : 10.1007/s00205-008-0122-8

URL : https://hal.archives-ouvertes.fr/hal-00806349

A. Farina, On the classification of solutions of the Lane???Emden equation on unbounded domains of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.5, pp.537-561, 2007.
DOI : 10.1016/j.matpur.2007.03.001

R. Filippucci, P. Pucci, and F. Robert, On a p-Laplace equation with multiple critical nonlinearities, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.2, pp.156-177, 2009.
DOI : 10.1016/j.matpur.2008.09.008

I. Fragaì-a, F. Gazzola, and B. Kawohl, Existence and nonexistence results for anisotropic quasilinear elliptic equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.21, issue.5, pp.715-734, 2004.
DOI : 10.1016/j.anihpc.2003.12.001

I. Fragaì-a, F. Gazzola, and G. Lieberman, Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains, Discrete Contin, Dyn. Syst, pp.280-286, 2005.

B. Franchi, E. Lanconelli, and J. Serrin, Existence and Uniqueness of Nonnegative Solutions of Quasilinear Equations inRn, Advances in Mathematics, vol.118, issue.2, pp.177-243, 1996.
DOI : 10.1006/aima.1996.0021

J. García-melián, J. D. Rossi, and J. C. , Large solutions to an anisotropic quasilinear elliptic problem, Annali di Matematica Pura ed Applicata, vol.71, issue.9, pp.689-712, 2010.
DOI : 10.1007/s10231-010-0132-7

F. Gazzola, Critical growth quasilinear elliptic problems with shifting subcritical perturbation, Differential Integral Equations, vol.14, issue.5, pp.513-528, 2001.

M. Guedda and L. Véron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal, pp.879-902, 1989.
DOI : 10.1016/0362-546x(89)90020-5

F. Q. Li, Anisotropic elliptic equations in L m, J. Convex Anal, vol.8, issue.2, pp.417-422, 2001.

G. M. Lieberman, Gradient estimates for a new class of degenerate elliptic and parabolic equations, Ann. Scuola Norm, Gradient estimates for anisotropic elliptic equations, pp.497-522, 1994.

P. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, Rev The concentration-compactness principle in the calculus of variations. The limit case, Mat. Iberoamericana, vol.134, issue.1, pp.145-201, 1985.

M. Mih?-ailescu, P. Pucci, and V. , Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent, Journal of Mathematical Analysis and Applications, vol.340, issue.1, pp.687-698, 2008.
DOI : 10.1016/j.jmaa.2007.09.015

M. Mih?-ailescu, V. , and S. Tersian, Eigenvalue problems for anisotropic discrete boundary value problems, Journal of Difference Equations and Applications, vol.231, issue.6, pp.557-567, 2009.
DOI : 10.1070/IM1987v029n01ABEH000958

Y. V. Namlyeyeva, A. E. Shishkov, and I. I. Skrypnik, Abstract, Advanced Nonlinear Studies, vol.6, issue.4, pp.617-641, 2006.
DOI : 10.1515/ans-2006-0407

J. Rákosník, Some remarks to anisotropic Sobolev spaces. I, Beiträge Anal, pp.55-68, 1979.

I. I. Skrypnik, Removability of an isolated singularity for anisotropic elliptic equations with absorption, Sbornik: Mathematics, vol.199, issue.7, pp.1033-1050, 2008.
DOI : 10.1070/SM2008v199n07ABEH003952

A. S. Tersenov and A. S. Tersenov, The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations, Journal of Differential Equations, vol.235, issue.2, pp.376-396, 2007.
DOI : 10.1016/j.jde.2007.01.009

M. Troisi, Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat, vol.18, pp.3-24, 1969.

J. Vétois, A priori estimates for solutions of anisotropic elliptic equations, Nonlinear Anal, pp.3881-3905, 2009.

J. Weickert, Anisotropic diffusion in image processing, European Consortium for Mathematics in Industry, B. G. Teubner, 1998.