Stability results for some nonlinear elliptic equations involving the p-laplacian with critical Sobolev growth
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 559-575. 
@article{COCV_1999__4__559_0,
     author = {Nazaret, Bruno},
     title = {Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical {Sobolev} growth},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {559--575},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1746167},
     zbl = {0930.35051},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_1999__4__559_0/}
}
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Nazaret, Bruno. Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical Sobolev growth. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 559-575. http://archive.numdam.org/item/COCV_1999__4__559_0/

[1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geom. 11 ( 1976) 573-598. | MR | Zbl

[2] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampere equations, Springer-Verlag ( 1982) (Grundlehren) 252. | MR | Zbl

[3] O. Druet, Generalized scalar curvature type equations on compact riemaniann manifolds. Preprint of the University of Cergy-Pontoise ( 1997). | MR

[4] F. Demengel and E. Hebey, On some nonlinear equations involving the p-Laplacian with critical Sobolev growth. Adv. in PDE's, to appear. | MR | Zbl

[5] P. Courilleau and F. Demengel, On the heat flow for p-harmonic maps with values in S1. Nonlinear Anal. TMA, accepted.

[6] M. Guedda and L. Veron, Local and global properties of solutions of quasilinear elliptic equations. J. Differential Equations 76 ( 1988) 159-189. | MR | Zbl

[7] M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponentsNonlinear Analysis, Theory, Methods and Applications 13 ( 1989) 879-902. | MR | Zbl

[8] E. Hebey and M. Vaugon, Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth. J. Funct. Anal. 119 ( 1994) 298-318. | MR | Zbl

[9] L.C. Evans, Weak convergence methods for nonlinear partial differential equations. Conference Board of the Mathematical Sciences 74 ( 1990). | MR | Zbl

[10] E. Hebey, La methode d'isométries-concentration dans le cas d'un problème non linéaire sur les variétés compactes à bord avec exposant critique de sobolev. Bull. Sci. Math. 116 ( 1992) 35-51. | MR | Zbl

[11] E. Hebey, Sobolev Spaces on Riemannian Manifolds, Springer-Verlag ( 1996) (LNM) 1635. | MR | Zbl

[12] A. Jourdain, Solutions nodales pour des équations de type courbure scalaire sur la sphère. Preprint of the University of Cergy-Pontoise ( 1997).

[13] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part I. Revista Matematica Iberoamericana 1 ( 1985) 145-199. | MR | Zbl

[14] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part II. Revista Matematica Iberoamericana 1 ( 1985) 45-116. | MR | Zbl

[15] B. Nazaret, Stabilité sous des perturbations visqueuses des solutions d'équations du type p-Laplacien avec exposant critique de Sobolev. Preprint of the University of Cergy-Pontoise (5/98).

[16] G. Talenti. Best constants in Sobolev inequalities. Ann. Mat. Pura Appl. 110 ( 1976) 353-372. | MR | Zbl

[17] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 ( 1984) 126-150. | MR | Zbl

[18] J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12 ( 1984) 191-202. | MR | Zbl