C. O. Alves, Positive solutions to quasilinear equations involving critical exponent on perturbed annular domains, Electron, J. Differential Equations, vol.13, issue.13, p.pp. (electronic), 2005.

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.

A. Bahri and J. Coron, On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain, Communications on Pure and Applied Mathematics, vol.75, issue.3, pp.253-294, 1988.
DOI : 10.1002/cpa.3160410302

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

M. Bendahmane and K. H. Karlsen, Renormalized solutions of an anisotropic reaction-diffusion-advection system with L 1 data [12] , 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.

O. V. Besov, Embeddings of an anisotropic Sobolev space for a domain with a flexible horn condition, Proc. Steklov Inst, pp.3-14, 1988.

L. Boccardo, T. Gallouët, and P. Marcellini, Anisotropic equations in L 1, Differential Integral Equations, vol.9, issue.1, pp.209-212, 1996.

L. Boccardo, P. Marcellini, and C. Sbordone, L ? -regularity for variational problems with sharp nonstandard growth conditions, Boll. Un. Mat. Ital. A, vol.4, issue.7 2, pp.219-225, 1990.

H. Brézis and J. Coron, Convergence of solutions of H-systems or how to blow bubbles, Archive For Rational Mechanics And Analysis, vol.133, issue.1, pp.21-56, 1985.
DOI : 10.1007/BF00281744

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

H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical sobolev exponents, Communications on Pure and Applied Mathematics, vol.22, issue.4, pp.437-477, 1983.
DOI : 10.1002/cpa.3160360405

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 On some nonlinear equations involving the p-Laplacian with critical Sobolev growth and perturbation terms, Adv. Differential Equations Appl. Anal, vol.323, 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.

O. Druet, E. Hebey, and F. Robert, Blow-up theory for elliptic PDEs in Riemannian geometry, Mathematical Notes, vol.45, 2004.
DOI : 10.1515/9781400826162

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

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.

N. Ghoussoub, Duality and perturbation methods in critical point theory, Cambridge Tracts in Mathematics, vol.107, 1993.
DOI : 10.1017/CBO9780511551703

M. Guedda and L. Véron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal, pp.879-902, 1989.

J. Ha?kovec and C. Schmeiser, A note on the anisotropic generalizations of the Sobolev and Morrey embedding theorems, Monatshefte f??r Mathematik, vol.20, issue.46, pp.71-79, 2009.
DOI : 10.1007/s00605-008-0059-x

S. N. Kruzhkov and I. M. , Kolod¯ ?? ?, On the theory of anisotropic Sobolev spaces, Uspekhi Mat, NaukRussian Russ. Math. Surveys, vol.38, issue.38 2, pp.207-208, 1983.

S. N. Kruzhkov and A. G. Korolev, On embedding theory for anisotropic function spaces, Dokl. Akad. Nauk SSSRRussian Dokl, vol.285, issue.32 3, pp.1054-1057, 1985.

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.146, issue.1, pp.145-201, 1985.

V. Lu, On imbedding theorems for spaces of functions with partial derivatives of various degrees of summability, Vestnik Leningrad, Univ, vol.16, issue.7, pp.23-37, 1961.

P. Marcellini, Regularity and existence of solutions of elliptic equations with p,q-growth conditions, Journal of Differential Equations, vol.90, issue.1, pp.1-30, 1991.
DOI : 10.1016/0022-0396(91)90158-6

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, Some remarks to anisotropic Sobolev spaces. II, Beiträge Anal, pp.55-68, 1979.

O. Rey, A multiplicity result for a variational problem with lack of compactness, Nonlinear Anal, pp.1241-1249, 1989.

J. Sacks and K. K. Uhlenbeck, The Existence of Minimal Immersions of 2-Spheres, The Annals of Mathematics, vol.113, issue.1, pp.1-24, 1981.
DOI : 10.2307/1971131

N. Saintier, Asymptotic estimates and blow-up theory for critical equations involving the p-Laplacian, Calculus of Variations and Partial Differential Equations, vol.51, issue.1, pp.299-331, 2006.
DOI : 10.1007/s00526-005-0344-7

R. M. Schoen, Variational theory for the total scalar curvature functional for riemannian metrics and related topics, Lecture Notes in Math, vol.12, issue.3, pp.120-154, 1987.
DOI : 10.1007/BF01208277

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

M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Variational methods: Applications to nonlinear partial differential equations and Hamiltonian systems, pp.511-517, 1984.
DOI : 10.1007/BF01174186

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, Asymptotic stability, convexity, and Lipschitz regularity of domains in the anisotropic regime Existence and regularity for critical anisotropic equations with critical directions, Strong maximum principles for anisotropic elliptic and parabolic equations, pp.71-3881, 2009.

H. C. Wente, Large solutions to the volume constrained plateau problem, Archive for Rational Mechanics and Analysis, vol.75, issue.1, pp.59-77, 1980.
DOI : 10.1007/BF00284621

S. Yan, A global compactness result for quasilinear elliptic equation involving critical Sobolev exponent, Chinese J. Contemp. Math, vol.16, issue.3, pp.227-234, 1995.