First eigenvalue for the p-Laplace operator

Nonlinear Analysis, Theory, Methods and Applications

Volumn 39, Issue 8, 2000, Pages 1051-1068

  Matei, Ana Maria ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING; VARIATIONAL TECHNIQUES;

ISOPERIMETRIC INEQUALITIES; LAPLACE OPERATOR;

NONLINEAR EQUATIONS;

EID: 0034148992     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00266-1     Document Type: Article

References (18)

1. P. Berard, Spectral geometry, direct and inverse problems, in: Lecture Notes in Mathematics, Vol. 1207, Springer, Berlin, 1986.
2. P. Berard, D. Meyer, Inégalités isopérimétriques et applications, Ann. Scient. Ec. Norm. Sup. 4e Ser. 15 (1982) 513-542.
3. M. Berger, P. Gauduchon, E. Mazet, Le spectre d'une variété Riemanniene, Lecture Notes in Mathematics, Vol. 194, Springer, Berlin, 1971.
4. R. Bishop, R. Crittenden, Geometry of Manifolds, Academic Press, New York, 1964.
5. H. Brezis, Analyse Fonctionelle, Théorie et Applications, Barcelone, Masson, 1993.
6. P. Buser, A note on the isoperimetric constant, Ann. Scient. Ec. Norm. Sup. 4e Ser. T. 15 (1982) 213-230.
7. J. Cheeger, The relation belween the Laplacian and the diameter for manifolds of non-negative curvature, Arch. Math. XIX (1968) 558-560.
8. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, in: Problems in Analysis, Princeton University Press, Princeton, NJ, 1970, pp. 195-199.
9. S.Y. Cheng, Eigenvalue comparison theorems and its geometric aplications, Math. Z. 143 (1975) 289-297.
10. S.-Y. Cheng, Eigenfunctions and eigenvalues of Laplacian, Proc. Symp. Pure Mathematics, Vol. 27, 1975, pp. 185-193.
11. S. Gallot, A sobolev inequality and some geometric application, in: Spectra of Riemannian Manifolds, Kaigai Publ., 1983, pp. 45-55.
12. J.P. Garzia Azorero, I. Peral Alonso, Existence and nonuniqueness for the p-Laplacian eigenvalues, Comm. Part. Diff. Equ. 12 (1987) 1389-1430.
13. M. Gromov, Paul Levy's Isoperimetric Inequality, Publications IHES, 1980.
14. S. Ilias, Constantes explicites pour les inegalites de Sobolev sur les Variétés Riemanniennes compactes, Ann. Inst. Fourier Grenoble 33 (2) (1983) 151-165.
15. p-2u=0, Research Reports, vol. A 263, Helsinki Univ. Tech. Inst. Math., Helsinki, 1988.
16. M. Otani, A remark on certain nonlinear elliptic equations, Proc. Faculty Sci., Tokai University, vol. XIX, 1984, pp. 23-28.
17. P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Diff. Equ. 51 (1984) 126-150.
18. L. Veron, Some existence and uniqueness results for solution of some quasilinear elliptic equations on compact Riemannian manifolds, Colloquia Mathematica Societatis Janos Bolyai, Vol. 62, P.D.E., Budapest, 1991, pp. 317-352.