Uniqueness results for nonlinear elliptic equations with a lower order term

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 2, 2005, Pages 153-170

  Betta, M Francesca ^a   Mercaldo, Anna ^b   Murat, François ^c   Porzio, M Michaela ^d  

^a UNIVERSITY OF NAPLES PARTHENOPE   (Italy)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^d SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Noncoercive problems; Nonlinear elliptic equations; Uniqueness; Weak solutions

Indexed keywords

FUNCTIONS; SET THEORY;

BOUNDED OPEN SUBSET; NONLINEAR ELLIPTIC EQUATIONS;

NONLINEAR EQUATIONS;

EID: 27544480392     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.03.097     Document Type: Article

References (19)

1. M. Artola, Sur une classe de problèmes paraboliques quasi-linéaires, Boll. Un. Mat. Ital. 5-B (1986) 51-70.
2. M. Artola, L. Tartar, Un résultat d'unicité pour une classe de problèmes paraboliques quasi-linéaires, Ricerche Mat. 44 (1995) 409-420.
3. G. Barles, A.P. Blanc, C. Georgelin, M. Kobylanski, Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 28 (1999) 381-404.
4. G. Barles, F. Murat, Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions, Arch. Rational Mech. Anal. 133 (1995) 77-101.
5. 1 (Ω), ESAIM Control Optim. Calc. Var. 8 (2002) 239-272 (special issue dedicated to the memory of Jacques-Louis Lions).
6. M.F. Betta, A. Mercaldo, F. Murat, M.M. Porzio, Existence of renormalized solutions to nonlinear elliptic equations with a lower-order term and right-hand side a measure, J. Math. Pures Appl. 82 (2003) 90-124.
7. L. Boccardo, Uniqueness of solutions for some nonlinear Dirichlet problems, Proceedings of the Conference to Celebrate the 65th Birthday of M. Artola, Bordeaux, 1997, to appear.
8. L. Boccardo, T. Gallouët, F. Murat, Unicité de la solution de certaines équations elliptiques non linéaires, C. R. Acad. Sci. Paris Sér. I 315 (1992) 1159-1164.
9. G. Bottaro, M.E. Marina, Problema di Dirichlet per equazioni ellittiche di tipo variazionale su insiemi non limitati, Boll. Un. Mat. Ital. 8 (1973) 46-56.
10. J. Carrillo, M. Chipot, On some nonlinear elliptic equations involving derivatives of nonlinearity, Proc. Roy. Soc. Edinburgh A 100 (1985) 281-294.
11. M. Chipot, G. Michaille, Uniqueness results and monotonicity properties for strongly nonlinear elliptic variational inequalities, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1989) 137-166.
12. T. Del Vecchio, M.M. Porzio, Existence results for a class of non coercive Dirichlet problems, Ricerche Mat. 44 (1995) 421-438.
13. T. Del Vecchio, M.R. Posteraro, An existence result for nonlinear and noncoercive problems, Nonlinear Anal. 31 (1998) 191-206.
14. J. Droniou, Non-coercive linear elliptic problems, Potential Anal. 17 (2002) 181-203.
15. J. Leray, J.-L. Lions, Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. France 93 (1965) 97-107.
16. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod et Gauthier-Villars, Paris, 1969.
17. O. Lopez-Pouso, M.M. Porzio, Linear elliptic problems with mixed boundary conditions related to radiation heat transfer, Math. Models Methods Appl. Sci. 12 (2002) 541-565.
18. A. Mokrane, F. Murat, The Lewy-Stampacchia's inequality for bilateral problems, Ricerche Mat. 53 (2004) 139-182.
19. A. Porretta, Uniqueness and homogenization for a class of operators in divergence form, Atti Sem. Mat. Fis. Univ. Modena 46 (1998) 915-936 (supplement dedicated to Professor C. Vinti).