On some nonlinear equations involving the p-laplacian with critical Sobolev growth

Advances in Differential Equations

Volumn 3, Issue 4, 1998, Pages 533-574

  Demengel, Françoise ^a   Hebey, Emmanuel ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

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[No Author keywords available]

Indexed keywords

EID: 0001511734     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geometry, 11 (1976), 573-598.
2. A. Bahri and J.M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure and Appl. Math., 41 (1988), 253-294.
3. H. Brézis, Nonlinear elliptic equations involving the critical Sobolev exponent, Survey and perspectives, Directions in Partial Differential Equations, Proceedings of a symposium [1985, Madison], 17-36. New York, Academic Press, 1987, Publications of the Mathematics Research Center, 54.
4. H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
5. L.C. Evans, Weak convergence methods for nonlinear partial differential equations, Conference Board of the Mathematical Sciences, 74, 1990.
6. S. Granlund, P. Lindqvist, and O. Martio, Conformally invariant variational integrals, Transactions of the American Mathematical Society, 277 (1983), 43-73.
7. M. Guedda and L. Veron, Local and global properties of solutions of quasilinear elliptic equations, Journal of Differential Equations, 76 (1988), 159-189.
8. M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Analysis, Theory, Methods and Applications, 13 (1989), 879-902.
9. E. Hebey, La méthode d'isométries-concentration dans le cas d'un problème non linéaire sur les variétés compactes à bord avec exposant critique de Sobolev, Bulletin des Sciences Mathématiques, 116 (1992), 35-51.
10. E. Hebey, Asymptotics for some quasilinear elliptic equations, Differential and Integral Equations, 9 (1996), 71-88.
11. E. Hebey and M. Vaugon, Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth, Journal of Functional Analysis, 119 (1994), 298-318.
12. J.L. Lewis, Regularity of the derivatives of solutions to certain degenerate elliptic equations, Indiana University Mathematics Journal, 32 (1983), 849-858.
13. G. Talenti, Best constants in Sobolev inequality, Ann. di Matem. Pura ed Appl., 110 (1976), 353-372.
14. P. Tolksdorf, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. in Partial Differential Equations, 8 (1983), 773-817.
15. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Journal of Differential Equations, 51 (1984), 126-150.
16. J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim., 12 (1984), 191-202.
17. L. Veron, Some existence and uniqueness results for solution of some quasilinear elliptic equations on compact Riemannian manifolds, Colloquia Mathematica Societatis Janos Bolyai, 62, Differential Equations, Budapest, 1991.