On the Liouville property for fully nonlinear equations

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 17, Issue 2, 2000, Pages 219-245

  Cutrì, Alessandra ^a   Leoni, Fabiana ^b  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038173085     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(00)00109-8     Document Type: Article

References (25)

1. Bahri A., Lions P.L., Solutions of superlinear elliptic equations and their Morse indexes, Comm. Pure Appl. Math. 45 (1992) 1205-1215.
2. Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série I 317 (1993) 945-950.
3. Berestycki H., Capuzzo Dolcetta L, Nirenberg L., Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal. 4 (1994) 59-78.
4. Birindelli I., Capuzzo Dolcetta I., Cutrì A., Liouville theorems for semilinear equations on the Heisenberg group, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 14 (3) (1997) 295-308.
5. Birindelli I., Capuzzo Dolcetta I., Cutrì A., Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, Comm. Partial Differential Equations 23 (7-8) (1998) 1123-1157.
6. Birindelli I., Mitidieri E., Liouville theorems for elliptic inequalities and applications, Proc. Royal Soc. Edinburgh 128A (1998) 1217-1247.
7. Caffarelli L.A., Interior a priori estimates for solutions of fully nonlinear equations, Ann. Math. 130 (1989) 189-213.
8. Caffarelli L.A., Cabré X., Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, Vol. 43, AMS, Providence, RI, 1995.
9. Capuzzo Dolcetta I., Teoremi di Liouville e stime a priori per equazioni ellittiche semilineari, Rend. Sem. Mat. Fis. Milano, to appear.
10. Capuzzo Dolcetta I., Cutrì A., On the Liouville property for sub-laplacians, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 25 (1-2) (1997) 239-256.
11. Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992) 1-67.
12. Cutrì A., Problemi semilineari ed integro-differenziali per sublaplaciani, Ph.D. Thesis, Universitá di Roma Tor Vergata, 1997.
13. Gidas B., Spruck J., A priori bounds for positive solutions of nonlinear elliptic equations, Comm. PDE 8 (1981) 883-901.
14. Gidas B., Spruck J., Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 35 (1981) 525-598.
15. Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983.
16. Ishii H., Lions P.L., Viscosity solutions of fully nonlinear second order elliptic partial differential equations, J. Differential Equations 83 (1990) 26-78.
17. Hörmander L., Notions of Convexity, Progress in Mathematics, Vol. 127, Birkhäuser, Boston, MA, 1994.
18. Lanconelli E., Uguzzoni F., Asymptotic behaviour and non existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group, Boll. Unione Mat. Ital., Sez B 8 (1) (1998).
19. Leoni F., work in preparation.
20. Pucci C., Operatori ellittici estremanti, Ann. Mat. Pura Appl. 72 (1966) 141-170.
21. Frotter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice Hall, 1967.
22. Ramos M., Terracini S., Troestler C., Problèmes elliptiques surlinéaires avec non-linéarité sans signe défini, C. R. Acad. Sci. Paris, Série I 325 (1997) 283-286.
23. Trudinger N.S., Lectures on nonlinear elliptic equations of second order, in: Lectures in Mathematical Sciences, The University of Tokyo, 1995.
24. Uguzzoni F., A Liouville-type theorem on halfspaces for the Kohn laplacian, Proc. Amer. Math. Soc. 127 (1) (1999) 117-123.
25. Uguzzoni F., A non existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group, NODEA 6 (2) (1999).