An existence result for nonlinear and noncoercive problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 31, Issue 1-2, 1998, Pages 191-206

  Del Vecchio, T ^a   Posteraro, M R ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Nonlinear elliptic equations

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; SET THEORY;

NONLINEAR ELLIPTIC EQUATIONS; SYMMETRIZATION TECHNIQUES;

NONLINEAR EQUATIONS;

EID: 0031602498     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00304-5     Document Type: Article

References (25)

1. Stampacchia, G., Equations elliptiques du second ordre à coefficients discontinus. Séminaire de Mathématiques Superieures. Les Presses de l'Université de Montreal, Montreal, 1966.
2. Maz'ja, V. G., On weak solutions of the Dirichlet and Neumann problems. Trans. Moscow Math. Soc., 1969, 20, 135-172.
3. Talenti, G., Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa, 1976, 3(4), 697-718.
4. Talenti, G., Nonlinear elliptic equations, rearrangements of functions and Orlicz spaces. Ann. Mat. Pura Appl., 1979, 120(4), 159-184.
5. Talenti, G., Linear elliptic P.D.E.: level sets, rearrangements and a priori estimates of solutions. Boll. Un. Mat. Ital., 1985, 4-B(6), 917-949.
6. Alvino, A., Lions, P. L. and Trombetti, G., Comparison results for elliptic and parabolic equations via Schwartz symmetrization. Ann. Inst. H. Poincaré, 1990, 7(2), 37-65.
7. Betta, M. F., Ferone, V. and Mercaldo, A., Regularity for solutions of nonlinear elliptic equations. Bull. Sci. Math. Dip. Mat. Appl. Universita' di Napoli. (To appear.)
8. Boccardo, L. and Gallouet, T., Nonlinear elliptic and parabolic equations involving measure data. Journal of Functional Analysis, 1989, 87(1), 149-169.
9. Boccardo, L. and Gallouet, T., Nonlinear elliptic equations with right-hand side measure. Comm. in P.D.E., 1992, 17(3, 4), 641-654.
10. Del Vecchio, T. and Porzio, M. M., Existence results for a class of noncoercive Dirichlet problems. Ricerche di Matematica. (To appear.)
11. Leray, J. and Lions, J. L., Quelques résultats de Visik sur les problémes elliptiques non linéaires par les méthodes de Minty-Browder. Bull. Soc. Math. France, 1965, 93, 97-107.
12. Lions, J. L. and Stampacchia, G., Variational inequalities. Commun. on Pure Appl. Math., 1967, XX, 493-519.
13. Bottaro, G., Alcune condizioni sufficienti per l'esistenza e l'unicita' della soluzione di una disequazione variazionale non coerciva. Ann. Mat. Pura Appl., Serie IV, 1975, 187-203.
14. Rakotoson, J. M., Quasilinear elliptic problems with measures as data. Differential and Integral Equations, 1991, 4(3), 449-457.
15. Del Vecchio, T., Nonlinear elliptic equations with measure data. Potential Analysis, 1995, 4, 185-203.
16. Del Vecchio, T. and Posteraro, M. R., Existence and regularity results for nonlinear elliptic equations with measure data. Advances in Differential Equations. (To appear.)
17. Bennett, C. and Sharpley, R., Interpolation of Operators. Academic Press, 1988.
18. Beckenback, E. and Bellman. R., Inequalities. Springer-Verlag, 1965.
19. Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities. Cambridge University Press, Cambridge, 1964.
20. Alvino, A. and Trombetti, G., Sulle migliori costanti di maggiorazione per una classe di equazioni ellittiche degeneri. Ricerche Mat., 1978, 27, 413-428.
21. Betta, M. F. and Mercaldo, A., Comparison and regularity results for a nonlinear elliptic equation. Nonlinear Analysis, 1993, 20(1), 63-77.
22. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris 1969.
23. Boccardo, L. and Murat, F., Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations. Nonlinear Analysis, 1992, 19(6), 581-597.
24. Giaquinta, M. and Giusti, E., Quasi-minima. Ann. Inst. H. Poincaré (Analyse non lineare), 1984, 1, 79-107.
25. Ladyzens'kaja, O. A. and Uraltceva, N. N., Linear and Quasilinear Elliptic Equations. Academic Press, New York, 1968.